% This is an example bibliography file for FPSAC submissions.

@article{ANigroUpdate,
    AUTHOR = {Abreu, Alex Corr\^ea and Nigro, Antonio},
     TITLE = {An update on {H}aiman's conjectures},
   JOURNAL = {Forum Math. Sigma},
  FJOURNAL = {Forum of Mathematics. Sigma},
    VOLUME = {12},
      YEAR = {2024},
     PAGES = {Paper No. e86, 15 pp.}, 
       DOI = {10.1017/fms.2024.86},
       URL = {https://doi.org/10.1017/fms.2024.86},
}

@Unpublished{ANigroPLV,
  author = 	 "A. Abreu and A. Nigro",
  title = 	 "Parabolic {Lusztig} varieties and chromatic symmetric functions",
  note =	 "Preprint {\tt math.AG/2212.13497} on {ArXiv}",
  year =	 2022
}

@Unpublished{ANigroSplit,
  author = 	 "A. Abreu and A. Nigro",
  title = 	 "Splitting the cohomology of {Hessenberg} varieties and $e$-positivity of chromatic symmetric functions",
  note =	 "Preprint {\tt math.AG/2304.10644} on {ArXiv}",
  year =	 2023
}

@article {AAERCharFormulasHyper,
    AUTHOR = {Adin, Ron M. and Athanasiadis, Christos A. and Elizalde, Sergi
              and Roichman, Yuval},
     TITLE = {Character formulas and descents for the hyperoctahedral group},
   JOURNAL = {Adv. in Appl. Math.},
  FJOURNAL = {Advances in Applied Mathematics},
    VOLUME = {87},
      YEAR = {2017},
     PAGES = {128--169},
   MRCLASS = {05E10 (05A05 05E05 15B34 20C30)},
  MRNUMBER = {3629266},
MRREVIEWER = {Jian-yi Shi},
       DOI = {10.1016/j.aam.2017.01.004},
       URL = {https://doi.org/10.1016/j.aam.2017.01.004},
}

@article {ABRDescentReps,
    AUTHOR = {Adin, Ron M. and Brenti, Francesco and Roichman, Yuval},
     TITLE = {Descent representations and multivariate statistics},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {357},
      YEAR = {2005},
    NUMBER = {8},
     PAGES = {3051--3082},
   MRCLASS = {20C30 (05E10 13A50 20F55)},
  MRNUMBER = {2135735},
MRREVIEWER = {Ira Gessel},
       DOI = {10.1090/S0002-9947-04-03494-4},
       URL = {https://doi.org/10.1090/S0002-9947-04-03494-4},
}

@article {ABPTrace,
    AUTHOR = {Aguirre, Juli{\'a}n and Bilbao, Mikel and Peral, Juan Carlos},
     TITLE = {The trace of totally positive algebraic integers},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {75},
      YEAR = {2006},
    NUMBER = {253},
     PAGES = {385--393 (electronic)},
     CODEN = {MCMPAF},
   MRCLASS = {11R06 (11Y40)},
  MRNUMBER = {MR2176405},
MRREVIEWER = {Christopher Smyth},
}

@Book{AMO,
  author = 	 "R. K. Ahuja and T. L. Magnanti and J. B. Orlin",
  title = 	 "{Network Flows: Theory, Algorithms, and Applications}",
  publisher = 	 "Prentice-Hall",
  year = 	 1993
}
		  
@Article{ASW,
  author = 	 "M. Aissen and I. J. Schoenberg and A. Whitney",
  title = 	 "On generating functions of totally positive sequences",
  journal =	 "J. Anal. Math.",
  year =	 1952,
  volume =	 2,
  pages =	 "93-103"
}

@article {AllenNewBases,
    AUTHOR = {Allen, Edward E.},
     TITLE = {New bases for the decomposition of the graded left regular
              representation of the reflection groups of type {$B\sb n$} and
              {$D\sb n$}},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {173},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {122--143},
}

@unpublished {AFultonDLoci,
    AUTHOR = {Anderson, David and Fulton, William},
     TITLE = {Degeneracy loci, pfaffians, and vexillary signed permutations},
    NOTE = {Preprint {\tt math.AG:1210.2066} on {ArXiv}},
    YEAR = {2012},
}


@article {AFultonVexRevisited,
    AUTHOR = {Anderson, David and Fulton, William},
     TITLE = {Vexillary signed permutations revisited},
   JOURNAL = {Algebr. Comb.},
  FJOURNAL = {Algebraic Combinatorics},
    VOLUME = {3},
      YEAR = {2020},
    NUMBER = {5},
     PAGES = {1041--1057},
   MRCLASS = {05A05 (05E16)},
  MRNUMBER = {4166808},
MRREVIEWER = {Yan\ Zhuang},
       DOI = {10.5802/alco.122},
       URL = {https://doi.org/10.5802/alco.122},
}

@Article{Ando,
  author = 	 "T. Ando",
  title = 	 "Totally positive matrices",
  journal =	 "Linear Algebra Appl.",
  year =	 1987,
  volume =	 90,
  pages =	 "165-219"
}
		  	
@Unpublished{ARSDoce,
  author = 	 "F. Ardila and M. Rosas and M. Skandera",
  title = 	 "Doce lecciones en combinatoria algebraica",
  note =	 "in progress",
  year =	 2003
}

@article {AK,
    AUTHOR = {Ariki, Susumu and Koike, Kazuhiko},
     TITLE = {A {H}ecke algebra of {$({\bf Z}/r{\bf Z})\wr{\mathfrak S}_n$} and
              construction of its irreducible representations},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {106},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {216--243},
   MRCLASS = {20C15 (20F55)},
  MRNUMBER = {1279219},
MRREVIEWER = {Andrzej Daszkiewicz},
       DOI = {10.1006/aima.1994.1057},
       URL = {https://doi.org/10.1006/aima.1994.1057},
}


@Article{ArmEcon,
  author = 	 "W.E. Armstrong",
  title = 	 "The determinateness of the utility function",
  journal =	 "Economic Journal",
  year =	 1939,
  volume =	 49,
  pages =	 "453--467"
}
		  		  
@Book{Artin,
  author = 	 "M. Artin",
  title = 	 "Algebra",
  publisher = 	 "Prentice-Hall",
  year = 	 1991,
  address =	 "Englewood Cliffs"
}
	
@article {AthanPSE,
    AUTHOR = {Athanasiadis, Christos A.},
     TITLE = {Power sum expansion of chromatic quasisymmetric functions},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {22},
      YEAR = {2015},
    NUMBER = {2},
      NOTE = {Paper 2.7, 9 pages},
   MRCLASS = {05E05 (05C30 05C31)},
  MRNUMBER = {3359910},
MRREVIEWER = {Jia Huang},
}

@Book{AM,
  author = 	 "M.F. Atiyah and I.G. Macdonald",
  title = 	 "{Commutative Algebra}",
  publisher = 	 "Addison-Wesley",
  year = 	 1969,
  address =	 "London"
}	  
		  
@Article{Baake,
  author = 	 "M. Baake",
  title = 	 "Structure and representations of the hyperoctahedral group",
  journal =	 "J.~Math.~Phys.",
  year =	 1984,
  volume =	 25,
  pages = 	 "3171--3182"
}

@Article{BabSteingPattern,
  author = 	 "Eric Babson and Einar {Steingr\'\i msson}",
  title = 	 "Generalized permutation patterns and a
		  classification of the {Mahonian statistics}",
  journal =	 "S\'em. Lothar. Combin.",
  year =	 2000,
  volume =	 44,
  note = 	 {Art.\ B44b, 18 pp. (electronic)}
}

		  
@Unpublished{BRB,
  author = 	 "Kenneth Baclawski and Gian-Carlo Rota and Sara Billey",
  title = 	 "{Introduction to the Theory of Probability}",
  note = 	 "MIT course notes for 18.313",
  year =	 1990
}


@article {BalaCharTables,
    AUTHOR = {Balasubramanian, K.},
     TITLE = {Character tables  of $n$-dimensional hyperoctahedral groups
     and their applications},
   JOURNAL = {J.~Math.~Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {114},
      YEAR = {2016},
    NUMBER = {10},
     PAGES = {1619--1633},
}

@article {BalaComp,
    AUTHOR = {Balasubramanian, K.},
     TITLE = {Computational multinomial combinatorics for coloring of $5d$-hypercubes for all irreducible representations and applications},
   JOURNAL = {J.~Math.~Chem.},
  FJOURNAL = {Journal of Mathematical Chemistry},
    VOLUME = {57},
      YEAR = {2019},
     PAGES = {655--689},
}


@unpublished{BCPerverse,
  AUTHOR = {Balibanu, Ana and Crooks, Peter},
   TITLE = {Perverse sheaves and the cohomology of regular {Hessenberg} varieties},
    NOTE = {Preprint {\tt math.RT:2004.07970} on {ArXiv}},
    YEAR = {2020},
    }


@article {BarVogPrim,
    AUTHOR = {Barbasch, Dan and Vogan, David},
     TITLE = {Primitive ideals and orbital integrals in complex exceptional
              groups},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {80},
      YEAR = {1983},
    NUMBER = {2},
     PAGES = {350--382},
}

@Incollection{BarcRam,
  author = 	 "H. Barcelo and A. Ram",
  title = 	 "Combinatorial Representation Theory",
  editor =       "G. C. Rota",
  year =	 1999,
  booktitle =    "New Perspectives in Algebraic Combinatorics 
                  (Berkeley, CA 1996-97)",
  series =       "Math. Sci. Res. Inst. Publ",
  publisher =    "Cambridge University Press",
  address =      "Cambridge",
  volume =       38,
  pages =	 "23--90"
}		  

@article{BJMajor,
  author = { Wayne W. Barrett and Charles R. Johnson },
  title = {Majorization monotonicity of symmetrized {F}ischer products},
  journal = {Linear and Multilinear Algebra},
  volume = {34},
  number = {1},
  pages = {67-74},
  year  = {1993},
  publisher = {Taylor & Francis},
  doi = {10.1080/03081089308818211},
}

@Article{BayerBill,
  author = 	 "Margaret M. Bayer and Louis J. Billera",
  title = 	 "Counting faces and chains in polytopes and posets",
  journal =	 "Contemp. Math.",
  year =	 1984,
  volume =	 34,
  pages =	 "207-252"
}

@Book{BJSLP,
  author = 	 "M. Bazaraa and J. Jarvis and H. Sherali",
  title = 	 "{Linear Programming and Network Flows}",
  publisher = 	 "Wiley",
  year = 	 1990
}		  
		 				  
@Article{BeilBern,
  author = 	 "A. Beilinson and J. Bernstein",
  title = 	 "Localization of $\mathfrak{g}$-modules",
  journal =	 "C. R. Acad.Sci. Paris Ser. {I} Math",
  year =	 1981,
  volume =	 292,
  pages =	 "15-18"
}

@incollection {BBDFaisceaux,
    AUTHOR = {Be\u{\i}linson, A. A. and Bernstein, J. and Deligne, P.},
     TITLE = {Faisceaux pervers},
 BOOKTITLE = {Analysis and topology on singular spaces, {I} ({L}uminy,
              1981)},
    SERIES = {Ast\'{e}risque},
    VOLUME = {100},
     PAGES = {5--171},
 PUBLISHER = {Soc. Math. France, Paris},
      YEAR = {1982},
   MRCLASS = {32C38},
  MRNUMBER = {751966},
MRREVIEWER = {Zoghman Mebkhout},
}

@article{BLMGeo,
    AUTHOR = {Be{\u\i}linson, A. A. and Lusztig, G. and MacPherson, R.},
     TITLE = {A geometric setting for the quantum deformation of {${\rm
              GL}_n$}},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {61},
      YEAR = {1990},
    NUMBER = {2},
     PAGES = {655--677},
}

		  
@Article{BellSkanMulti,
  author = 	 "J. Bell and M. Skandera",
  title = 	 "Multicomplexes and polynomials with real zeros",
  year =	 2007,
  journal =	 "Discrete Math.",
  volume =       307,
  number =       6,
  pages =        "668--682"
}

@Article{Benzer,
  author = 	 "S. Benzer",
  title = 	 "On the topology of the genetic fine structure",
  journal =	 "Proc. Nat. Acad. Sci.",
  year =	 1959,
  volume =	 45,
  pages =	 "1607--1620"
}

@article {BFZParamCB,
    AUTHOR = {Berenstein, Arkady and Fomin, Sergey and Zelevinsky, Andrei},
     TITLE = {Parametrizations of canonical bases and totally positive
              matrices},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {122},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {49--149},
}
		
@Article{BerZelCan,
  author = 	 "A. Berenstein and A. Zelevinsky",
  title = 	 "Canonical bases for the quantum groups of type {$A_r$}
                 and piecewise linear combinatorics",
  journal =	 "Duke Math. J.",
  year =	 1996,
  volume =	 82,
  pages =	 "473--502"
}


@Article{BerZelString,
  author = 	 "A. Berenstein and A. Zelevinsky",
  title = 	 "String bases for quantum groups of type {$A_r$}",
  journal =	 "Adv. Sov. Math.",
  year =	 1993,
  volume =	 16,
  number =       1,		  
  pages =	 "51--89"
}

@article {BerZelTPSchubert,
    AUTHOR = {Berenstein, Arkady and Zelevinsky, Andrei},
     TITLE = {Total positivity in {S}chubert varieties},
   JOURNAL = {Comment. Math. Helv.},
  FJOURNAL = {Commentarii Mathematici Helvetici},
    VOLUME = {72},
      YEAR = {1997},
    NUMBER = {1},
     PAGES = {128--166}
}
		  
@Book{BergeGHG,
  author = 	 "C. Berge",
  title = 	 "{Graphs and Hypergraphs}",
  publisher = 	 "North-Holland",
  year = 	 1976
}		  
		
@article{BBHTDecomp,
    AUTHOR = {Bergeron, F. and Bergeron, N. and Howlett, R. B. and Taylor,
              D. E.},
     TITLE = {A decomposition of the descent algebra of a finite {C}oxeter
              group},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {1},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {23--44}
}
 				  
@article {FBergConjLR,
    AUTHOR = {Bergeron, Fran{\c{c}}ois and Biagioli, Riccardo and Rosas,
              Mercedes H.},
     TITLE = {Inequalities between {L}ittlewood-{R}ichardson coefficients},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {113},
      YEAR = {2006},
    NUMBER = {4},
     PAGES = {567--590},
     CODEN = {JCBTA7},
   MRCLASS = {05E05},
  MRNUMBER = {MR2216453},
}

@Unpublished{FBergMcPosDiff,
  author = 	 "F. Bergeron and P. McNamara",
  title = 	 "Some positive differences of products of {Schur} functions",
  note =	 "Preprint {\tt math.CO/0412289} on {ArXiv}",
  year =	 2005
}


@Article{NBergCCSchubert,
  author = 	 "Nantel Bergeron",
  title = 	 "A Combinatorial Construction of the {Schubert} Polynomials",
  journal =	 "J. Combin. Theory Ser. A",
  year =	 1992,
  volume =	 " 60",
  pages =	 "168--182"
}


@Article{NBergSotMonoid,
  author = 	 "Nantel Bergeron  and Frank Sottile",
  title = 	 "A monoid for the universal k-Bruhat order",
  journal =	 "Preprint",
  year =	 1997,
  month =	 "June"
}

@Article{NBergBilleyRC,
  author = 	 "Nantel Bergeron and Sara Billey",
  title = 	 "{RC-graphs and Schubert polynomials}",
  journal =	 "Experimental Mathematics",
  year =	 1993,
  volume =	 2,
  number =	 4,
  pages =	 "257--269"
}

@Article{BGG,
  author = 	 " I.N. Bernstein and  I.M. Gelfand and S.I. Gelfand",
  title = 	 "{Schubert cells and cohomology of the spaces
		  $G/P$}", 
  journal =	 "Russian Math. Surveys",
  year =	 1973,
  number =	 3,
  volume =	 28,
  pages =	 "1--26"
}

@Article{BGG2,
  author = 	 " I.N. Bernstein and  I.M. Gelfand and S.I. Gelfand",
  title = 	 "{Structure of representations generated by highest
		  weight vectors}", 
  journal =	 "Funct. Anal. and Appl.",
  year =	 1971,
  volume =	 5,
  pages =	 "1--8"
}

@unpublished{BillBrentiQuasi,
  author = 	 "Louis J. Billera and Francesco Brenti",
  title = 	 "Quasisymmetric functions and {Kazhdan-Lusztig} polynomials",
  year =	 2007,
  note =         {Preprint {\tt math.CO/0710.3965v1} on {ArXiv}}
}


@Incollection{BillBjornFace,
  author = 	 "Louis J. Billera and Anders Bj{\"o}rner",
  title = 	 "Face numbers of polytopes and complexes",
  year =	 1997,
  booktitle =	 "Handbook of Discrete and Computational Geometry",
  editor =	 "J. E. Goodman and J. O'Rourke",
  publisher = 	 "CRC Press",
  address =      "Boca Raton/New York",
  pages =	 "291-310"
}


@Article{BJS,
  author = 	 "Sara Billey and  W. Jockusch and R. Stanley",
  title = 	 "Some Combinatorial Properties of {Schubert} Polynomials",
  year =	 1993,
  journal =	 "J. Algebraic Combin.",
  volume =	 2,
  pages =	 "345-374"
}

@Article{BH,
  author = 	 "Sara Billey and M. Haiman",
  title = 	 "{Schubert polynomials for the classical groups}",
  journal =	 "J. Amer. Math. Soc.",
  year =	 1995,
  volume =	 8,
  pages =	 "443-482"
}


@Article{B2,
  author = 	 "Sara Billey",
  title = 	 "{Kostant polynomials and the cohomology ring for $G/B$}",
  year =	 1997,
  journal =	 "Proc. Nat.  Acad. Sci. U.S.A.",
  volume =	 1,
  pages =	 "29-32"
}

		  
@book{BilleyLak,
    AUTHOR = {Billey, Sara and Lakshmibai, V.},
     TITLE = {Singular loci of {S}chubert varieties},
    SERIES = {Progress in Mathematics},
    VOLUME = {182},
 PUBLISHER = {Birkh\"auser Boston Inc.},
   ADDRESS = {Boston, MA},
      YEAR = {2000},
     PAGES = {xii+251},
}

@Article{BilleyPattern,
  author = 	 "S. C. Billey",
  title = 	 "Pattern avoidance and rational smoothness of {Schubert} varieties",
  journal =	 "Adv. Math.",
  volume =       139,
  year =	 1998,
  pages =        "141--156"
}

@article {BilleyLamVex,
    AUTHOR = {Billey, Sara and Lam, Tao Kai},
     TITLE = {Vexillary elements in the hyperoctahedral group},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {8},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {139--152},
   MRCLASS = {05E05 (05E15 20F10)},
  MRNUMBER = {1648468},
MRREVIEWER = {Witold\ Kra\'{s}kiewicz},
       DOI = {10.1023/A:1008633710118},
       URL = {https://doi.org/10.1023/A:1008633710118},
}


@Article{BWHex,
  author = 	 "S. C. Billey and G. Warrington",
  title = 	 "{Kazhdan-Lusztig} polynomials for $321$-hexagon-avoiding permutations",
  journal =	 "J. Algebraic Combin.",
  volume =       13,
  number =       2,
  year =	 2001,
  pages =        "111--136"
}


@Inproceedings{BjBruhat,
  author = 	 "A. {Bj\"orner}",
  title = 	 "Orderings of {Coxeter} groups",
  year =	 1984,
  editor =       "C. Greene",
  booktitle =    "Combinatorics and Algebra",
  series =       "Contemp. Math",
  volume =       "34",
  publisher =    "American Mathematical Society",
  address =      "Providence, RI",
  pages =	 "175--195"
}		  


@Article{BjBrentiBruhat,
  author =       "A. {Bj\"orner} and F. Brenti",
  title =        "An improved tableau criterion for {Bruhat} order",
  journal =      "Electron. J. Combin.",
  year =          1996,
  volume =        3,
  number =        1,
  note =         {Research paper 22, 5 pp.\ (electronic)}
}		  
		
@Book{BBCoxeter,
    AUTHOR = {Bj\"orner, Anders and Brenti, Francesco},
     TITLE = {Combinatorics of {C}oxeter groups},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {231},
 PUBLISHER = {Springer, New York},
      YEAR = {2005},
     PAGES = {xiv+363}, 
}


@Article{BFS,
  author =       "A. {Bj\"orner} and P. Frankl and R. Stanley",
  title =        "The number of faces of balanced {Cohen-Macaulay}
                   complexes and a generalized {Macaulay} theorem",
  journal =      "Combinatorica",
  year =          1987,
  volume =        7,
  pages =         "23-34"
}		  

@Incollection{BGSIntroCM,
  author = 	 "Anders Bj{\"o}rner and Adriano Garsia and Richard Stanley",
  title = 	 "An introduction to the theory of {Cohen-Macaulay} posets",
  booktitle =	 "Ordered Sets",
  year =	 1982,
  editor =       "I. Rival",
  publisher =    "Reidel",
  address =      "Dordrecht/Boston/London",
  pages =	 "583--615"
}

@Article{BjWPermStats,
  author = 	 "Anders Bj{\"o}rner and Michelle Wachs",
  title = 	 "Permutation Statistics and Linear Extensions of Posets",
  journal =	 "J. Combin. Theory Ser. A",
  year =	 1991,
  volume =	 58,
  number =	 1,
  pages =	 "85-114"
}

@Book{Bodmer,
  author = 	 "F. Bodmer",
  title = 	 "{The Loom of Language}",
  editor =       "L. Hogben",
  publisher = 	 "Norton",
  year = 	 1944
}		  

@article{BoeKLH,
    AUTHOR = {Boe, Brian D.},
     TITLE = {Kazhdan-{L}usztig polynomials for {H}ermitian symmetric
              spaces},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {309},
      YEAR = {1988},
    NUMBER = {1},
     PAGES = {279--294}
}

@Article{Bogart22,
  author = 	 "K. Bogart",
  title = 	 "An obvious proof of {Fishburn's} interval order theorem",
  journal =	 "Discrete Math",
  year =	 1992,
  volume =	 118,
  pages =	 "239--242"
}		  
		 
@Book{Bogart,
  author = 	 "K. Bogart",
  title = 	 "{Introductory Combinatorics}",
  publisher = 	 "Hartcourt Brace Jovanovich",
  year = 	 1998
}		  

@Misc{BogartComm,
  author = 	 "K. Bogart",
  year =         "2001",
  note = 	 "Personal communication"
}		  
		  
@Book{BollMGT,
  author = 	 "B. Bollob\'as",
  title = 	 "{Modern Graph Theory}",
  publisher = 	 "Springer",
  year = 	 1998
}		  
		 		

@Article{bona98,
  author = 	 "Mikl\'os B\'ona",
  title = 	 "The permutation classes equinumerous to the Smooth class",
  journal =	 "Electron. J. Combin.",
  year =	 1998,
  volume =	 5,
  note =	 "Research paper 31, 12 pp.\ (electronic)"
}

@book{BonaCP,
    AUTHOR = {B{\'o}na, Mikl{\'o}s},
     TITLE = {Combinatorics of permutations},
    SERIES = {Discrete Mathematics and its Applications (Boca Raton)},
      NOTE = {With a foreword by Richard Stanley},
 PUBLISHER = {Chapman \& Hall/CRC, Boca Raton, FL},
      YEAR = {2004},
}

@book{BonaIntroEC,
    AUTHOR = {B{\'o}na, Mikl{\'o}s},
     TITLE = {Introduction to enumerative combinatorics},
    SERIES = {Walter Rudin Student Series in Advanced Mathematics},
      NOTE = {With a foreword by Richard Stanley},
 PUBLISHER = {McGraw Hill Higher Education, Boston, MA},
      YEAR = {2007},
}


@Article{BoochGen,
  author = 	 "A. Boocher and B. Froehle",
  title = 	 "On Generators of bounded ratios of minors for totally positive matrices",
  year =	 2008,
  volume =	 428,
  number=	 7,
  journal =	 "Linear Algebra Appl.",
  pages =        "1664--1684",
       DOI = {10.1016/j.laa.2007.10.011},
       URL = {https://doi.org/10.1016/j.laa.2007.10.011},
}

@Techreport{BoothCol,
  author = 	 "K. S. Booth and C. J. Colborn",
  title = 	 "Problems polynomially equivalent to {GRAPH ISOMORPHISM}",
  year =	 1979,
  number =       "CS-77-04",
  institution =  "Dept. of Computer Science, University of Waterloo",
  address =      "Waterloo, Canada"
}
		  
@Book{borel,
  author = 	 "A. Borel",
  title = 	 "{Intersection Cohomology}",
  publisher = 	 "Birkh{\"a}user",
  year = 	 1984
}		  
		  
@Book{bou,
  author = 	 "N. Bourbaki",
  title = 	 "{Groups et Algebres de Lie}",
  publisher = 	 "Masson",
  year = 	 1957
}


@article {BourchWeather,
    AUTHOR = {Bourchtein, Andrei and Bourchtein, Ludmila and Naumov, Maxim},
     TITLE = {On correctness of the vertical discretization in numerical
              weather prediction models},
   JOURNAL = {Appl. Math. Comput.},
  FJOURNAL = {Applied Mathematics and Computation},
    VOLUME = {158},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {513--527},
     CODEN = {AMHCBQ},
   MRCLASS = {34A12 (93B35)},
  MRNUMBER = {MR2094636 (2005e:34005)},
MRREVIEWER = {Sanjeeva Balasuriya},
}

@Article{BradMacPMoment,
  author = 	 "Tom Braden and Robert MacPherson",
  title = 	 "From moment maps to intersection cohomology",
  journal =	 "Math. Ann.",
  year =	 2001,
  volume =	 321,
  number =	 3,
  pages =	 "533-551"
}

@article {BrandCounter,
    AUTHOR = {Br{\"a}nd{\'e}n, Petter},
     TITLE = {Counterexamples to the {N}eggers-{S}tanley conjecture},
   JOURNAL = {Electron. Res. Announc. Amer. Math. Soc.},
  FJOURNAL = {Electronic Research Announcements of the American Mathematical
              Society},
    VOLUME = {10},
      YEAR = {2004},
     PAGES = {155--158 (electronic)},
   MRCLASS = {06A07 (05A15)},
  MRNUMBER = {MR2119757 (2005j:06002)},
MRREVIEWER = {Mikl{\'o}s B{\'o}na},
}

@Article{BrandSG,
  author = 	 "P. Br{\"a}nd{\'e}n",
  title = 	 "Sign-graded posets, unimodality of {$W$}-polynomials, and the {Charney-Davis} conjecture",
  journal =	 "Electron. J. Combin.",
  volume =       11,
  number =       2,
  note =         "Research paper 9, 15 pp.\ (electronic)",	   
  year =	 "2005"
}


@Book{BrentiPol,
  author = 	 "Francesco Brenti",
  title = 	 "Unimodal, Log-Concave, and {P\'olya} Frequency Sequences in
Combinatorics",
  series =	 "Mem. Amer. Math. Soc",
  publisher =    "American Mathematical Society",
  address =      "Providence, RI", 
  year =	 1989,
  number =	 413
}


@InCollection{BrentiConv,
  author = 	 "Francesco Brenti",
  title = 	 "The applications of total positivity to combinatorics, and conversely",
  booktitle =	 "Total Positivity and its Applications",
  publisher =	 "Kluwer Acad. Publ.",
  year =	 1994,
  pages =	 "451--473",
  volume =	 359
}

@Article{Brenti94,
  author = 	 "Francesco Brenti",
  title = 	 "A combinatorial formula for {Kazhdan-Lusztig} polynomials",
  journal =	 "Invent.~Math.",
  year =	 1994,
  volume =	 118,
  number =	 2,
  pages =	 "371--394"
}

@Article{BrentiCTP,
  author = 	 "Francesco Brenti",
  title = 	 "Combinatorics and Total Positivity",
  journal =	 "J.~Combin.~Theory Ser.~A",
  year =	 1995,
  volume =	 71,
  number =	 2,
  pages =	 "175--218"
}


@Article{Brenti97,
  author = 	 "Francesco Brenti",
  title = 	 "Combinatorial expansions of {Kazhdan-Lusztig} polynomials",
  journal =	 "J. London Math. Soc.",
  year =	 1997,
  volume =	 55,
  number =	 2,
  pages =	 "448-472"
}

@Article{BrentiCPKL,
  author = 	 "Francesco Brenti",
  title = 	 "Combinatorial properties of the {Kazhdan-Lusztig} {$R$}-polynomials for {$S_n$}",
  journal =	 "Adv. Math.",
  year =	 1997,
  volume =	 126,
  number =	 1,
  pages =	 "21--51"
}

		  
@Article{BrentiKLPoint,
    AUTHOR = {Brenti, Francesco},
     TITLE = {Kazhdan-{L}usztig and {$R$}-polynomials from a combinatorial
              point of view},
      NOTE = {Selected papers in honor of Adriano Garsia (Taormina, 1994)},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {193},
      YEAR = {1998},
    NUMBER = {1-3},
     PAGES = {93--116},
}


@Article{BrentiKLRYD,
  author = 	 "Francesco Brenti",
  title = 	 "{K}azhdan-{L}usztig and {$R$}-polynomials, {Y}oung's lattice, and {D}yck partitions",
  journal =	 "Pacific J. Math.",
  pages =	 "257--286",
  volume =	 207,
  number =       2,
  year =	 "2002"
}

@article {BrentiKLHistory,
    AUTHOR = {Brenti, Francesco},
     TITLE = {Kazhdan-{L}usztig polynomials: history problems, and
              combinatorial invariance},
   JOURNAL = {S\'em. Lothar. Combin.},
  FJOURNAL = {S\'eminaire Lotharingien de Combinatoire},
    VOLUME = {49},
      YEAR = {2002/04},
     PAGES = {Art. B49b, 30 pp. (electronic)},
}
		
@Misc{BrentiComm,
  author = 	 "F. Brenti and V. Welker",
  year =         "2005",
  note = 	 "Personal communication"
}		  		  


@article {BChowUIODot,
    AUTHOR = {Brosnan, Patrick and Chow, Timothy Y.},
     TITLE = {Unit interval orders and the dot action on the cohomology of
              regular semisimple {H}essenberg varieties},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {329},
      YEAR = {2018},
     PAGES = {955--1001},
   MRCLASS = {05E05 (14M15)},
  MRNUMBER = {3783432},
MRREVIEWER = {Marko Radovanovi\'{c}},
       DOI = {10.1016/j.aim.2018.02.020},
       URL = {https://doi.org/10.1016/j.aim.2018.02.020},
}

@Book{Brualdi,
  author = 	 "R. Brualdi",
  title = 	 "{Introductory Combinatorics}",
  publisher = 	 "Prentice Hall",
  year = 	 1998
}		  

@article {BrundanKL,
    AUTHOR = {Brundan, Jonathan},
     TITLE = {Dual canonical bases and {K}azhdan-{L}usztig polynomials},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {306},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {17--46},
}
		
@Book{BHCM,
  author = 	 "W. Bruns and J. Herzog",
  title = 	 "{Cohen-Macaulay Rings}",
  publisher = 	 "Cambridge University Press",
  year = 	 1993,
  address =	 "London"
}		        	

@Unpublished{BryanFrIt,
  author = 	 "Whitney Suzanne Bryan",
  title = 	 "Comparison of Gender in French and Italian: A Historical Perspective",
  year =	 2001,
  note =      "Senior Thesis Projects, 1993--2002. Available at {\tt https://trace.tennessee.edu/utk{\textunderscore}interstp2/60}",
}


@Article{BryKash,
  author = 	 "J.-L. Brylinski and M. Kashiwara",
  title = 	 "Kazhdan-Lusztig conjectures and holonomic systems",
  journal =	 "Invent. Math.",
  year =	 1981,
  volume =	 64,
  pages =	 "387-410"
}

@Article{BSkanClausenKL,
  author = 	 "Charles Buehrle and Mark Skandera",
  title = 	 "Relations between the {Clausen} and {Kazhdan-Lusztig} 
                 representations of {$S_n$}",
  journal =	 "J.\ Pure Appl.\ Algebra",
  year =	 2010,
  volume =	 214,
  number =       5,
  pages =	 "689--700"
}		  

@Article{BEGW,
  author = 	 "Joe Buhler and David Eisenbud and Ron Graham and
		  Colin Wright",
  title = 	 "{Juggling Drops and Descents}",
  journal =	 "Amer.\ Math.\ Monthly",
  year =	 1994,
  volume =	 101,
  pages =	 "507--519"
}		  

@book{Bullen,
    AUTHOR = {Bullen, P. S.},
     TITLE = {Handbook of means and their inequalities},
    SERIES = {Mathematics and its Applications},
    VOLUME = {560},
      NOTE = {Revised from the 1988 original [P. S. Bullen, D. S.
              Mitrinovi\'c and P. M. Vasi\'c, {\it Means and their
              inequalities}, Reidel, Dordrecht; MR0947142]},
 PUBLISHER = {Kluwer Academic Publishers Group},
   ADDRESS = {Dordrecht},
      YEAR = {2003},
     PAGES = {xxviii+537},
   MRCLASS = {26-02 (26D15 26E60)},
  MRNUMBER = {MR2024343 (2005a:26001)},
MRREVIEWER = {Zsolt P{\'a}les},
}


@Article{Canfield80,
  author = 	 "E.R.Canfield",
  title = 	 "A Sperner property preserved by products",
  journal =	 "Linear and Multilinear Algebra",
  year =	 1980,
  volume =	 9,
  pages =	 "151--157"
}

@Article{Carqnos,
  author = 	 {L. Carlitz},
  title = 	 "{q-Bernoulli and Eulerian numbers}",
  journal = 	 {Trans. Amer. Math. Soc.},
  year = 	 1954,
  volume =	 76,
  pages =	 {332--350}
}
@Article{Carqpolys,
  author = 	 {L. Carlitz},
  title = 	 "{A combinatorial property of q-Eulerian numbers}",
  journal = 	 {American Math. Monthly},
  year = 	 1975,
  volume =	 82,
  pages =	 {51--54}
}
@Article{CarlitzSVRiseFallLevel,
  author =       {L. Carlitz and R. Scoville and T. Vaughan},
  title =        "{Enumeration of pairs of sequences by rises, falls, and levels}",
  journal =      {Manuscripta Math.},
  year =         {1976},
  volume =       {19},
  pages =        {211--243}
  }


@inproceedings{carlson1967,
    AUTHOR = {Carlson, David},
     TITLE = {Weakly sign-symmetric matrices and some determinantal
              inequalities},
   JOURNAL = {Colloq. Math.},
  FJOURNAL = {Colloquium Mathematicum},
    VOLUME = {17},
      YEAR = {1967},
     PAGES = {123--129}, 
       DOI = {10.4064/cm-17-1-123-129},
       URL = {https://doi.org/10.4064/cm-17-1-123-129},
}
  
  
@Article{carrell86,
  author = 	 {James B. Carrell},
  title = 	 {Orbits of the Weyl Group and a Theorem of DeConcini and Procesi},
  journal = 	 {Composito Mathematica},
  year = 	 1986,
  volume =	 60,
  pages =	 {45--52}
}

@Article{carrell86,
  author = 	 {James B. Carrell},
  title = 	 {Orbits of the Weyl Group and a Theorem of DeConcini and Procesi},
  journal = 	 {Composito Mathematica},
  year = 	 1986,
  volume =	 60,
  pages =	 {45--52}
}

@Article{carrell92,
  author = 	 {James B. Carrell},
  title = 	 {Some Remarks on regular Weyl Group Orbits and the Cohomology of Schubert Varieties},
  journal = 	 {Contemp. Mathematics},
  year = 	 1992,
  volume =	 139
}


@Article{carrell94,
  author = 	 "James B. Carrell",
  title = 	 "{The Bruhat graph of a Coxeter group, a conjecture of Deodhar, and rational smoothness of Schubert varieties}",
  journal = 	 "Proceedings of Symposia in Pure Math.",
  year = 	 1994,
  volume =	 56,
  number =	 "Part 1",
  pages =	 "53--61"
}

@book{CartierFoataProb,
    AUTHOR = {Cartier, P. and Foata, D.},
     TITLE = {Probl\`emes combinatoires de commutation et r\'earrangements},
    SERIES = {Lecture Notes in Mathematics, No. 85},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1969},
}

@article{CasColKL,
    AUTHOR = {Casian, Luis G. and Collingwood, David H.},
     TITLE = {The {K}azhdan-{L}usztig conjecture for generalized {V}erma
              modules},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {195},
      YEAR = {1987},
    NUMBER = {4},
     PAGES = {581--600},
     CODEN = {MAZEAX},
   MRCLASS = {17B10 (22E47)},
  MRNUMBER = {MR900346 (88i:17008)},
MRREVIEWER = {James E. Humphreys},
}

@Article{ChariMatroid,
  author = 	 "M. Chari",
  title = 	 "Matroid Inequalities",
  journal =	 "Discrete Math.",
  year =	 1995,
  volume =	 147,
  pages =	 "283-286"
}
		  
		  
@Article{ChariDecomp,
  author = 	 "M. Chari",
  title = 	 "Two decompositions in topological combinatorics with
		  applications to matroid complexes",
  journal =	 "Trans. Amer. Math. Soc.",
  year =	 1997,
  volume =	 349,
  number =       10,
  pages =	 "3925-3943"
}


@Article{CharneyDavis,
  author = 	 "R. Charney and M. Davis",
  title = 	 "The {Euler} characteristic of a nonpositively curved, 
                  piecewise {Euclidean} manifold",
  journal =	 "Pacific J. Math.",
  year =	 1995,
  volume =	 171,
  number =       1,
  pages =	 "117--137"
}

		  
@Article{ChaseSub,
  author = 	 "P. J. Chase",
  title = 	 "Subsequence numbers and logarithmic concavity",
  journal =	 "Discrete Math.",
  year =	 1976,
  volume =	 16,
  number =       2,
  pages =	 "123--140"
}

		  
@unpublished{ChenTNN,
  author = 	 "Charlie Chen",
  title = 	 "Total non-negativity and the search for an optimal criterion: from {Lindstr\"om's Lemma} to double wiring diagrams and chamber minors",
  year =	 2004,
  note =         "unpublished REU paper"
}


@Article{CHEV,
  author = 	 "C. Chevalley",
  title = 	 "{Sur les D\'{e}compositions Cellulaires des Espaces $G/B$}",
  journal =	 " Proceedings of Symposia in Pure Mathematics",
  year =	 1994,
  volume =	 56,
  number =	 1
}

@Unpublished{CHPos,
  author = 	 "Soojin Cho and Jaehyun Hong",
  title = 	 "Positivity of chromatic symmetric functions associated with {Hessenberg} functions of bounce number $3$",
  year =	 2019,
  note =         "Preprint {\tt math.CO/1910.07308v1} on {ArXiv}"
}


@Article{ChowDes,
  author = 	 "Tim Chow",
  title = 	 "Descents, Quasi-Symmetric Functions, {Robinson-Schensted} for Posets, and the Chromatic Symmetric Function",
  journal =	 "J. Algebraic Combin.",
  year =	 1999,
  volume =	 10,
  pages =	 "227-240"
}

@Unpublished{ChowNoteChrom,
  author = 	 "Tim Chow",
  title = 	 "A Note on a Combinatorial Interpretation of the $e$-Coefficients of the Chromatic Symmetric Function",
  year =	 1997,
  note =         "Preprint {\tt math.CO/1306.2400} on {ArXiv}"
}


@article{ChudSeyStable,
    AUTHOR = {Chudnovsky, Maria and Seymour, Paul},
     TITLE = {The roots of the independence polynomial of a clawfree graph},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {97},
      YEAR = {2007},
    NUMBER = {3},
     PAGES = {350--357},
   MRCLASS = {05C69},
  MRNUMBER = {2305888},
MRREVIEWER = {Steven D. Noble},
       URL = {https://doi.org/10.1016/j.jctb.2006.06.001},
}
		

@incollection {ChungBucky,
    AUTHOR = {Chung, Fan R. K. and Kostant, Bertram and Sternberg, Shlomo},
     TITLE = {Groups and the buckyball},
 BOOKTITLE = {Lie theory and geometry},
    SERIES = {Progr. Math},
    VOLUME = {123},
     PAGES = {97--126},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {1994},
}

@article {CiVacSuper,
    AUTHOR = {Cicalese, Ferdinando and Vaccaro, Ugo},
     TITLE = {Supermodularity and subadditivity properties of the entropy on
              the majorization lattice},
   JOURNAL = {IEEE Trans. Inform. Theory},
  FJOURNAL = {Institute of Electrical and Electronics Engineers.
              Transactions on Information Theory},
    VOLUME = {48},
      YEAR = {2002},
    NUMBER = {4},
     PAGES = {933--938},
}

@article {CMRIndexSpec,
    AUTHOR = {Coll, Jr., Vincent E. and Mayers, Nicholas W. and Russoniello,
              Nicholas},
     TITLE = {The index and spectrum of {L}ie poset algebras of types {B},
              {C}, and {D}},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {28},
      YEAR = {2021},
    NUMBER = {3},
     NOTE = {Paper 3.47, 23 pages},
   MRCLASS = {17B20 (05E16 06A11 17B30)},
  MRNUMBER = {4311410},
MRREVIEWER = {Weijia\ Wang},
       DOI = {10.37236/9558},
       URL = {https://doi.org/10.37236/9558},
}

@Article{ClFoECalc1,
  author = 	 "Robert J. Clarke and Dominique Foata",
  title = 	 "{Eulerian calculus I: univariable statistics}",
  journal =	 "Europ. J. Combin.",
  year =	 1994,
  volume =	 15,
  pages =	 "345--362"
}		 
		  
		  
@Article{ClFoECalc2,
  author = 	 "Robert J. Clarke and Dominique Foata",
  title = 	 "{Eulerian calculus II: an extension of Han's
		  fundamental transformation}",
  journal =	 "Europ. J. Combin.",
  year =	 1995,
  volume =	 16,
  pages =	 "221--252"
}

		  
@Article{ClFoECalc3,
  author = 	 "Robert J. Clarke and Dominique Foata",
  title = 	 "{Eulerian calculus III: the ubiquitous Cauchy formula}",
  journal =	 "Europ. J. Combin.",
  year =	 1995,
  volume =	 16,
  pages =	 "329--355"
}

		  
@Article{ClFoECalc4,
  author = 	 "Robert J. Clarke and Dominique Foata",
  title = 	 "{Eulerian calculus IV: specializations}",
  journal =	 "S\'em. Lothar. Combin.",
  year =	 1994,
  volume =	 32,
  note =        {Art. B32b, approx.\ 12 pp.\ (electronic)}
}

		  
@Article{ClSteing,
  author = 	 "Robert J. Clarke and Einar {Steingr\' \i msson} and J. Zeng",
  title = 	 "New {Euler-Mahonian} Statistics on Permutations and Words", 
  journal =	 "Adv. Appl. Math.",
  year =	 1997,
  volume =	 18,
  pages =	 "237--270"
}

@article {ClausenDOCO,
    AUTHOR = {Clausen, Michael},
     TITLE = {Dominance orders, {C}apelli operators, and straightening of
              bideterminants},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {5},
      YEAR = {1984},
    NUMBER = {3},
     PAGES = {207--222},
   MRCLASS = {05A17 (15A72)},
  MRNUMBER = {MR765627 (86a:05008)},
MRREVIEWER = {J. D{\'e}sarm{\'e}nien},
}
		
@article {ClausenMPST,
    AUTHOR = {Clausen, Michael},
     TITLE = {Multivariate polynomials, standard tableaux, and
              representations of symmetric groups},
      NOTE = {Invariant-theoretic algorithms in geometry (Minneapolis, MN,
              1987)},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {11},
      YEAR = {1991},
    NUMBER = {5-6},
     PAGES = {483--522},
}

		  
@incollection{CSSPathTabFPSAC,
    AUTHOR = {Clearman, Sam and Shelton, Brittany and Skandera, Mark},
     TITLE = {Path tableaux and combinatorial interpretations of immanants 
for class functions of {$S_n$}},
 BOOKTITLE = {23rd {I}nternational {C}onference on {F}ormal {P}ower {S}eries
              and {A}lgebraic {C}ombinatorics ({FPSAC} 2011)},
    SERIES = {Discrete Math.\ Theor.\ Comput.\ Sci.\ Proc., AO},
     PAGES = {233--244},
 PUBLISHER = {Assoc.\ Discrete Math.\ Theor.\ Comput.\ Sci., Nancy},
      YEAR = {2011}
}

@Unpublished{CSkanTNNCharArx,
  author = 	 {Clearwater, Adam and Skandera, Mark},
  title = 	 {Total nonnegativity and {H}ecke algebra trace evaluations},
  year =	 {2019},
  NOTE = {Preprint {\tt math.CO/2007.14512v1} on {ArXiv}},
}

@article{CSkanTNNChar,
  author = 	 {Clearwater, Adam and Skandera, Mark},
  title = 	 {Total nonnegativity and {H}ecke algebra trace evaluations},
   JOURNAL = {Ann.\ Combin.},
  FJOURNAL = {Annals of Combinatorics}, 
  volume =	 25,
  PAGES = {757-787},
     YEAR = {2021},
}


@incollection {MR2958028,
    AUTHOR = {Shelton, Brittany and Skandera, Mark},
     TITLE = {Hecke algebra characters and quantum chromatic symmetric
              functions},
 BOOKTITLE = {24th {I}nternational {C}onference on {F}ormal {P}ower {S}eries
              and {A}lgebraic {C}ombinatorics ({FPSAC} 2012)},
    SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AR},
     PAGES = {551--562},
 PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
      YEAR = {2012},
   MRCLASS = {05E05},
  MRNUMBER = {2958028},
}


@Article{ClemLin,
  author = 	 "G. Clements and B. {Lindstr\" om}",
  title = 	 "A generalization of a combinatorial theorem of {Macaulay}", 
  journal =	 "J. Combin. Theory",
  year =	 1969,
  volume =	 7,
  pages =	 "230--238"
}


@unpublished{CMPChromatic,
  AUTHOR = {Colmenarejo, Laura and Morales, Alejandro and Panova, Greta},
   TITLE = {Chromatic symmetric functions of {Dyck paths} and $q$-rook theory},
    NOTE = {Preprint {\tt math.CO/2012.00913} on {ArXiv}},
    YEAR = {2020},
    }

		  		  
@Article{CryerProp,
  author = 	 "C. W. Cryer",
  title = 	 "Some properties of Totally positive matrices", 
  journal =	 "Linear Algebra Appl.",
  year =	 1976,
  volume =	 15,
  pages =	 "1--25"
}

@PhdThesis{CsarThesis,
  author = 	 "Sebastian Csar",
  title = 	 "Root and weight semigroup rings for signed posets",
  school = 	 "University of Minnesota",
  year = 	 2014,
  address =	 "Minneapolis, MN"
}


@article{CurtisLIT,
    AUTHOR = {Curtis, Charles W.},
     TITLE = {On {L}usztig's isomorphism theorem for {H}ecke algebras},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {92},
      YEAR = {1985},
    NUMBER = {2},
     PAGES = {348--365},
}

@Article{CurtisCircular,
  author = 	 "E. Curtis and D. V. Ingerman and J. Morrow",
  title = 	 "Circular planar graphs and resistor networks",
  journal =	 "Linear Algebra Appl.",
  year =	 1998,
  volume =	 283,
  pages =	 "115--150"
}

@article {CIKHecke,
    AUTHOR = {Curtis, C. W. and Iwahori, N. and Kilmoyer, R.},
     TITLE = {Hecke algebras and characters of parabolic type of finite
              groups with {$(B,$} {$N)$}-pairs},
   JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
  FJOURNAL = {Institut des Hautes \'Etudes Scientifiques. Publications
              Math\'ematiques},
    VOLUME = {40},
      YEAR = {1971},
     PAGES = {81--116}
}
		
@Unpublished{AllieThesis,
  author = 	 "A. Cuttler",
  title = 	 "Symmetric Mean Inequalities",
  year =	 2006,
  month =        "May",
  note =         "Haverford College undergraduate thesis"
}
 

@article {CGSSymmMean,
    AUTHOR = {Cuttler, Allison and Greene, Curtis and Skandera, Mark},
     TITLE = {Inequalities for symmetric means},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {32},
      YEAR = {2011},
    NUMBER = {6},
     PAGES = {745--761},
   MRCLASS = {05E05},
  MRNUMBER = {2821548 (2012k:05438)},
MRREVIEWER = {Trueman MacHenry},
       DOI = {10.1016/j.ejc.2011.01.020},
       URL = {http://dx.doi.org/10.1016/j.ejc.2011.01.020},
}

@unpublished{DahlbergTri,
  AUTHOR = {Dahlberg, Samantha},
   TITLE = {Triangular Ladders ${P}_{d,2}$ are $e$-positive},
    NOTE = {Preprint {\tt math.CO/1811.04885} on {ArXiv}},
    YEAR = {2018},
    }

@Article{DahlbergNewFormula,
  author = 	 "S. Dahlberg",
  title = 	 "A New formula for {Stanley's} chromatic symmetric function for unit interval graphs and e-positivity for triangular ladder graphs",
  journal =	 "S\'em. Lothar. Combin.",
  year =	 2019,
  volume =	 82,
  note =        {Art.\ B59, approx.\ 12 pp.\ (electronic) }		  
}

@Article{DatSkan,
  author = 	 "A.~Datko and M.~Skadera",
  title = 	 "Combinatorial interpretation of {Kazhdan-Lusztig}
basis elements indexed by $45312$-avoiding permutations in $S_6$",
  journal =	 "Pure Math.\ Appl.",
  year =	 2022,
  volume =	 30,
  pages =        "68--74"
}


@Article{DK,
  author = 	 "R. A. Dean and G. Keller",
  title = 	 "Natural Partial Orders",
  journal =	 "Canad.\ J.\ Math",
  year =	 1968,
  volume =	 20,
  pages =	 "535--554"
}

@article {DEPYoung,
    AUTHOR = {de Concini, C. and Eisenbud, David and Procesi, C.},
     TITLE = {Young diagrams and determinantal varieties},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {56},
      YEAR = {1980},
    NUMBER = {2},
     PAGES = {129--165},
}
		  
@Article{Dem,
  author = 	 "M. Demazure",
  title = 	 "{D\'esingularization des Vari\'et\'es de Schubert
		  G\'en\'eralis\'ees}", 
  journal =	 "Ann. Sc. E.N.S.",
  year =	 1974,
  volume =	 4,
  number =	 7,
  pages =	 "53--58"
}

@Article{Den1,
  author = 	 "M. Denert",
  title = 	 "The genus zeta function of hereditary orders in central
                 simple algebras over global fields", 
  journal =	 "Math. Comp.",
  year =	 1990,
  volume =	 54,
  pages =	 "449--465"
}

@article {DPSHessenberg,
    AUTHOR = {De Mari, F. and Procesi, C. and Shayman, M. A.},
     TITLE = {Hessenberg varieties},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {332},
      YEAR = {1992},
    NUMBER = {2},
     PAGES = {529--534},
   MRCLASS = {14L30 (14M17)},
  MRNUMBER = {1043857},
MRREVIEWER = {Michel\ Brion},
       DOI = {10.2307/2154181},
       URL = {https://doi.org/10.2307/2154181},
}

@article {DSGenEuler,
    AUTHOR = {De Mari, Filippo and Shayman, Mark A.},
     TITLE = {Generalized {E}ulerian numbers and the topology of the
              {H}essenberg variety of a matrix},
   JOURNAL = {Acta Appl. Math.},
  FJOURNAL = {Acta Applicandae Mathematicae. An International Journal on
              Applying Mathematics and Mathematical Applications},
    VOLUME = {12},
      YEAR = {1988},
    NUMBER = {3},
     PAGES = {213--235},
   MRCLASS = {05A10 (14M15 32M10 65F15)},
  MRNUMBER = {973945},
MRREVIEWER = {Naohisa\ Shimomura},
       DOI = {10.1007/BF00046881},
       URL = {https://doi.org/10.1007/BF00046881},
}

@Article{Deodhar77,
  author = 	 "V. Deodhar",
  title = 	 "Some characterizations of {Bruhat} ordering on a {Coxeter} 
                  group and determination of the relative {M\"obius} function",
  journal =	 "Invent. Math.",
  year =	 1977,
  volume =	 39,
  pages =	 "187--198"
}


		  
@Article{Deodhar85,
  author = 	 "V. Deodhar",
  title = 	 "Local Poincar\'e duality and non-singularity of Schubert varieties",
  journal =	 "Comm. Algebra",
  year =	 1985,
  volume =	 13,
  pages =	 "1379--1388"
}

@article {DeoGeoBO1,
    AUTHOR = {Deodhar, Vinay V.},
     TITLE = {On some geometric aspects of {B}ruhat orderings. {I}. {A}
              finer decomposition of {B}ruhat cells},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {79},
      YEAR = {1985},
    NUMBER = {3},
     PAGES = {499--511},
}

@article{DeoGeoBO2,
    AUTHOR = {Deodhar, Vinay},
     TITLE = {On some geometric aspects of {B}ruhat orderings. {II}. {T}he
              parabolic analogue of {K}azhdan-{L}usztig polynomials},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {111},
      YEAR = {1987},
    NUMBER = {2},
     PAGES = {483--506},
}

@Article{Deodhar90,
  author = 	 "Vinay Deodhar",
  title = 	 "A combinatorial setting for questions in
		  {Kazhdan--Lusztig} theory",
  journal =	 "Geom. Dedicata",
  year =	 1990,
  volume =	 36,
  number =	 1,
  pages =	 "95-119"		  
}
		  
@article{DeoDuality,
    AUTHOR = {Deodhar, Vinay},
     TITLE = {Duality in parabolic set up for questions in
              {K}azhdan-{L}usztig theory},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {142},
      YEAR = {1991},
    NUMBER = {1},
     PAGES = {201--209},
}

		  
@Article{Deodhar94,
  author = 	 "V. Deodhar",
  title = 	 "A brief survey of {Kazhdan-Lusztig} theory and
		  related topics",
  journal =	 "Proc. Sympos. Pure Math.",
  year =	 1994,
  volume =	 56,
  number =	 1
}

@Misc{DerksenComm,
  author = 	 "H. Derksen",
  year =         "2002",
  note = 	 "Personal communication"
}		  		  

@article{DKR,
    AUTHOR = {D{\'e}sarm{\'e}nien, J. and Kung, Joseph P. S. and Rota,
              Gian-Carlo},
     TITLE = {Invariant theory, {Y}oung bitableaux, and combinatorics},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {27},
      YEAR = {1978},
    NUMBER = {1},
     PAGES = {63--92},
   MRCLASS = {15A72 (14M15)},
  MRNUMBER = {MR0485944 (58 \#5737)},
MRREVIEWER = {A.-A. A. Jucys},
}

		  
@article {DStraight,
    AUTHOR = {D{\'e}sarm{\'e}nien, J.},
     TITLE = {An algorithm for the {R}ota straightening formula},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {30},
      YEAR = {1980},
    NUMBER = {1},
     PAGES = {51--68},
     CODEN = {DSMHA4},
   MRCLASS = {15A72},
  MRNUMBER = {MR561764 (82c:15034)},
MRREVIEWER = {G. D. James},
}

@article {DJRepHecke,
    AUTHOR = {Dipper, Richard and James, Gordon},
     TITLE = {Representations of {H}ecke algebras of general linear groups},
   JOURNAL = {Proc. London Math. Soc. (3)},
    VOLUME = {52},
      YEAR = {1986},
    NUMBER = {1},
     PAGES = {20--52}
}

@article {DJRepHeckeB,
    AUTHOR = {Dipper, Richard and James, Gordon},
     TITLE = {Representations of {H}ecke algebras of type {$B_n$}},
   JOURNAL = {J.\ Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {146},
      YEAR = {1992},
     PAGES = {454--481},
}

@article {DDFFAlmost,
    AUTHOR = {Doble, Christopher and Doignon, Jean-Paul and Falmagne, Jean-Claude and Fishburn, Peter},
     TITLE = {Almost connected orders},
   JOURNAL = {Order},
    VOLUME = {18},
      YEAR = {2001},
    NUMBER = {4},
     PAGES = {295--311}
}


@Misc{DobComm,
  author = 	 "E. Dobrowolski",
  year =         "2003",
  note = 	 "Personal communication"
}		  		  

@article {DobPylSupport,
    AUTHOR = {Dobrovolska, Galyna and Pylyavskyy, Pavlo},
     TITLE = {On products of {$\mathfrak{sl}\sb n$} characters and
              support containment},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {316},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {706--714},
}


@article {DoikouNuke,
    AUTHOR = {Doikou, Anastasia},
     TITLE = {From affine {H}ecke algebras to boundary symmetries},
   JOURNAL = {Nuclear Phys. B},
  FJOURNAL = {Nuclear Physics. B},
    VOLUME = {725},
      YEAR = {2005},
    NUMBER = {3},
     PAGES = {493--530},
     CODEN = {NUPBBO},
   MRCLASS = {81R50 (17B37 82B20)},
  MRNUMBER = {MR2166173 (2006f:81088)},
MRREVIEWER = {Rinat M. Kashaev},
}


@article {DomLenCCQM,
    AUTHOR = {Domokos, M. and Lenagan, T. H.},
     TITLE = {Conjugation coinvariants of quantum matrices},
   JOURNAL = {Bull. London Math. Soc.},
  FJOURNAL = {The Bulletin of the London Mathematical Society},
    VOLUME = {35},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {117--127},
}


@unpublished{DonPeter395,
  author = 	 "Perri Donenfeld and Kaitlyn Peterson",
  title = 	 "The symmetric group, the symmetric group algebra, the 
                 {Hecke} algebra, and pictoral representations", 
  year =	 2005,
  note =         "unpublished manuscript"
}


@article {DoubiletFOCT9,
    AUTHOR = {Doubilet, Peter and Rota, Gian-Carlo and Stein, Joel},
     TITLE = {On the foundations of combinatorial theory. {IX}.
              {C}ombinatorial methods in invariant theory},
   JOURNAL = {Studies in Appl. Math.},
    VOLUME = {53},
      YEAR = {1974},
     PAGES = {185--216},
}

@Article{DougInv,
    AUTHOR = {Douglass, J. Matthew},
     TITLE = {An inversion formula for relative {K}azhdan-{L}usztig
              polynomials},
   JOURNAL = {Comm. Algebra},
  FJOURNAL = {Communications in Algebra},
    VOLUME = {18},
      YEAR = {1990},
    NUMBER = {2},
     PAGES = {371--387}, 
       DOI = {10.1080/00927879008823919},
       URL = {https://doi.org/10.1080/00927879008823919},
}

@Article{DGSBruhat,
  author = 	 "B. Drake and S. Gerrish and M. Skandera",
  title = 	 "Two new criteria for comparison in 
                  the {Bruhat} order",
  journal =      "Electron. J. Combin.",
  volume =       11,
  number =       1,
  note =         "Note 6, 4 pp.",	   
  year =	 "2004",
       DOI = {10.37236/1847},
       URL = {https://doi.org/10.37236/1847},
}

@Article{DGSMNNBruhat,
  author = 	 "B. Drake and S. Gerrish and M. Skandera",
  title = 	 "Monomial nonnegativity and the {Bruhat} order",
  journal =      "Electron. J. Combin.",
  volume =       11,
  number =       2,
  note =         "Paper 18, 6 pp.\ (electronic)",	   
  year =	 "2004/06"
}


@article{DrinfeldQYBE,
  author  = {Drinfeld, V. G.},
  title   = {{H}opf algebras and the quantum {Y}ang-{B}axter equation},
  journal = {Dokl. Akad. Nauk. SSSR},
  volume  = {283},
  year    = {1985},
  number  = {5},
  pages   = {1060--1064},
}


@article{DuCBIrrRep,
    AUTHOR = {Du, Jie},
     TITLE = {Canonical bases for irreducible representations of quantum
              {${\rm GL}\sb n$}},
   JOURNAL = {Bull. London Math. Soc.},
  FJOURNAL = {The Bulletin of the London Mathematical Society},
    VOLUME = {24},
      YEAR = {1992},
    NUMBER = {4},
     PAGES = {325--334},
}

@article{DuCBIrrRep2,
    AUTHOR = {Du, Jie},
     TITLE = {Canonical bases for irreducible representations of quantum
              {${\rm GL}\sb n$}. {II}},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {51},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {461--470},
}
	
@article {DuGlobal,
    AUTHOR = {Du, Jie},
     TITLE = {Global {IC} bases for quantum linear groups},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {114},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {25--37},
     CODEN = {JPAAA2},
   MRCLASS = {17B37 (16W30)},
  MRNUMBER = {MR1425316 (98b:17013)},
MRREVIEWER = {Nicol{\'a}s Andruskiewitsch},
}

@incollection{DuICB,
    AUTHOR = {Du, Jie},
     TITLE = {{${\rm IC}$} bases and quantum linear groups},
 BOOKTITLE = {Algebraic groups and their generalizations: quantum and
              infinite-dimensional methods (University Park, PA, 1991)},
    SERIES = {Proc. Sympos. Pure Math},
    VOLUME = {56},
     PAGES = {135--148},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1994},
   MRCLASS = {17B37 (16W30 81R50)},
  MRNUMBER = {MR1278732 (95d:17010)},
MRREVIEWER = {Branislav Jur{\v{c}}o},
}

@incollection{DuKLITS,
    AUTHOR = {Du, Jie},
     TITLE = {Kazhdan-{L}usztig bases and isomorphism theorems for
              {$q$}-{S}chur algebras},
 BOOKTITLE = {Kazhdan-{L}usztig theory and related topics ({C}hicago, {IL},
              1989)},
    SERIES = {Contemp. Math},
    VOLUME = {139},
     PAGES = {121--140},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1992},
   MRCLASS = {17B37 (16S80 20G99 81R50)},
  MRNUMBER = {MR1197832 (94b:17019)},
MRREVIEWER = {Richard Dipper},
}
		
@article{DuNewPf,
    AUTHOR = {Du, Jie},
     TITLE = {A new proof for the canonical bases of type ${A}$},
   JOURNAL = {Algebra Colloq.},
    VOLUME = {6},
      YEAR = {1999},
    NUMBER = {4},
     PAGES = {377--383},
}


@Article{DumDmc,
  author = 	 "D. Dumont",
  title = 	 "{Interpr\'etations combinatoires des nombres de Genocchi}",
  journal =	 "Duke Math. J.",
  year =	 1974,
  volume =	 41,
  pages =	 "305-318"
}


@Article{DuvalComb,
  author = 	 "A. Duval",
  title = 	 "A combinatorial decomposition of simplicial complexes",
  journal =	 "Israel J. Math.",
  year =	 1994,
  volume =	 87,
  pages =	 "77--87"
}

@Article{DyerHASBI,
  author = 	 "M. J. Dyer",
  title = 	 "Hecke algebras and shellings of {Bruhat} intervals",
  journal =	 "Compositio Math.",
  year =	 1993,
  volume =	 89,
  pages =	 "91--115"
}

@Incollection{EulInst,
  author = 	 "L. Euler",
  title = 	 "Institutiones calculi differentialis",
  year =	 1913,
  booktitle =    "Opera Omnia, Series Prima",
  volume =	 "X",
  publisher =    "Verlag von B. G. Teubner",
  address =      "Leipzig"
}

@Article{EG,
  author = 	 "P. Edelman and C. Greene",
  title = 	 "{Balanced Tableaux}",
  journal =	 "Adv. Math.",
  year =	 1987,
  volume =	 63,
  pages =	 "42--99"
}

@Article{ER,
  author = 	 "P. Edelman and V. Reiner",
  title = 	 "{$H$-shellings and $h$-complexes}",
  journal =	 "Adv. Math.",
  year =	 1994,
  volume =	 106,
  pages =	 "36-64"
}

@Article{ELWQuasiSchur,
  AUTHOR = {Egge, Eric and Loehr, Nicholas and Warrington, Greg},
  TITLE = {From quasisymmetric expansions to {Schur} expansions via a
            modified inverse {Kostka} matrix},
  JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
  VOLUME = {31},
  YEAR = {2010},
  PAGES = {2014--2027},
  }

@article{EMR,
  author = 	 "Richard Ehrenborg and Margaret A. Readdy",
  title = 	 "{Juggling and applications to q-analogues}",
  journal =	 "preprint",
  year =	 "Feb. 3, 1995"
}		  


@article{EhrSteing,
  author = 	 "Richard Ehrenborg and Einar {Steingr\' \i msson}",
  title = 	 "The Excedance set of a permutation",
  journal =	 "preprint",
  year =	 "2000"
}		  

@article{Ehresmann,
  author = 	 "C. Ehresmann",
  title = 	 "Sur la topologie de certains espaces {homog\`enes}",
  journal =	 "Ann. Math.",
  volume =	 35,
  pages =	 "187-198",
  year =	 "1934"
}		  


@PhdThesis{KErik93,
  author = 	 "Kimmo Eriksson",
  title = 	 "Strongly convergent games and Coxeter groups",
  school = 	 "KTH",
  year = 	 1993,
  address =	 "Stockholm"
}
		  

@PhdThesis{HErik94,
  author = 	 "Henrik Eriksson",
  title = 	 "Computational and combinatorial aspects of Coxeter groups",
  school = 	 "KTH",
  year = 	 1994,
  address =	 "Stockholm"
}
		  		  
@Article{EPSWhichSVHV,
  author = 	 {Laura Escobar and Martha Precup and John Shareshian},
  title = 	 {Which {Schubert} varieties are {Hessenberg} varieties?},
  journal = 	 {Transform. Groups},
  year = 	 {To appear}
}

@Article{FGJMult,
  author = 	 "S. M. Fallat and M. I. Gekhtman and C. R. Johnson",
  title = 	 "Multiplicative principal-minor inequalities for
		  totally nonnegative matrices",
  journal =	 "Adv. in Appl. Math.",
  year =	 2003,
  volume =       30,
  number =       3,
  pages =        "442--470",
       DOI = {10.1016/S0196-8858(02)00506-7},
       URL = {https://doi.org/10.1016/S0196-8858(02)00506-7},
}

@incollection {FJDetAncient,
    AUTHOR = {Fallat, Shaun M. and Johnson, Charles R.},
     TITLE = {Determinantal inequalities: ancient history and recent
              advances},
 BOOKTITLE = {Algebra and its applications ({A}thens, {OH}, 1999)},
    SERIES = {Contemp. Math.},
    VOLUME = {259},
     PAGES = {199--212},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2000},
   MRCLASS = {15A15 (15A45)},
  MRNUMBER = {1778502},
       DOI = {10.1090/conm/259/04095},
       URL = {https://doi.org/10.1090/conm/259/04095},
}

@book {FJTNNMatrices,
    AUTHOR = {Fallat, Shaun M. and Johnson, Charles R.},
     TITLE = {Totally nonnegative matrices},
    SERIES = {Princeton Ser. Appl. Math.},
 PUBLISHER = {Princeton University Press, Princeton, NJ},
      YEAR = {2011},
     PAGES = {xvi+248}, 
       DOI = {10.1515/9781400839018},
       URL = {https://doi.org/10.1515/9781400839018},
}


@Article{FanStructHAQ,
  author = 	 "K. Fan",
  title = 	 "Structure of a {H}ecke algebra quotient",
  journal =	 "J. Amer. Math. Soc.",
  year =	 1997,
  volume =       10,
  number =       1,
  pages =        "139--167"
}

@Article{FanMon,
  author = 	 "K. Fan and R. M. Green",
  title = 	 "Monomials and {Temperley-Lieb} algebras",
  journal =	 "J. Algebra",
  year =	 1997,
  volume =       190,
  pages =        "498-517"
}

@Article{FarleyLERP,
  author = 	 "Jonathan Farley",
  title = 	 "Linear extensions of ranked posets, enumerated by descents.
A problem of {Stanley} from the 1981 {Banff} conference on ordered sets",
  year =	 2005,
  journal =	 "Adv. Appl. Math.",
  volume =	 34,
  number =       2,
  pages =	 "295--312"
}


@Misc{FinchComm,
  author = 	 "A. Finch",
  year =         "2005",
  note = 	 "Personal communication"		  
}
	
@unpublished{FinchKas395,
  author = 	 "A. Finch and L. Kasakoff",
  title = 	 "Math 395 final project", 
  year =	 2005,
  note =         "unpublished manuscript"
}

@article{fischer1908,
  title={{\"U}ber den {H}adamardschen {D}eterminantensatz},
  author={Fischer, E},
  journal={Arch. Math. (Basel)},
  volume={13},
  pages={32--40},
  year={1908}
}

@PhdThesis{SFischerThesis,
  author = 	 "Steven Fischer",
  title = 	 "Signed poset homology and $q$-analog {M\"obius} functions",
  school = 	 "University of Michigan",
  year = 	 1993,
  address =	 "Ann Arbor, MI"
}


@Book{Fish,
  author = 	 "P. C. Fishburn",
  title = 	 "{Interval Graphs and Interval Orders}",
  publisher = 	 "Wiley",
  year = 	 1985,
  address =	 "New York"
}

@Article{Fish70,
  author = 	 "P. C. Fishburn",
  title = 	 "Intransitive indifference with unequal indifference
                  intervals",
  journal =	 "J. Math. Psych.",
  year =	 1970,
  pages =        "144-149",
  volume =       7
}

@article {FishMonjWiener,
    AUTHOR = {Fishburn, Peter and Monjardet, Bernard},
     TITLE = {Norbert {W}iener on the theory of measurement (1914, 1915,
              1921)},
   JOURNAL = {J. Math. Psych.},
  FJOURNAL = {Journal of Mathematical Psychology},
    VOLUME = {36},
      YEAR = {1992},
    NUMBER = {2},
     PAGES = {165--184},
   MRCLASS = {92-03 (01A60 92J45)},
}
		

@Misc{FoComm,
  author = 	 "Dominique Foata",
  year =         "1999",
  note = 	 "Personal communication"
}


@Incollection{FoDist,
  author = 	 "D. Foata",
  title = 	 "Distributions {Eul\'eriennes} et {Mahoniennes} sur le
                  groupe des permutations",
  editor =       "M. Aigner",
  year =	 1977,
  booktitle =    "Higher Combinatorics",
  volume =	 19,
  publisher =    "D. Reidel Publishing Company",
  address =      "Dordrecht-Holland",
  pages =	 "27-49"
}

@Article{FoNet,
  author = 	 "D. Foata",
  title = 	 "{On the Netto inversion number of a sequence}",
  journal =	 "Proc.\ Amer.\ Math.\ Soc.",
  year =	 1968,
  volume =	 19,
  pages =	 "236--240"
}

@Article{FoHanSTC,
  author = 	 "D. Foata and G. Han",
  title = 	 "Une nouvelle transformation pour les statistiques {Euler-Mahoniennes} ensemblistes",
  journal =	 "Mosc. Math. J.",
  year =	 2004,
  volume =	 4,
  pages =	 "131--152"
}

@article {FHMaster1,
    AUTHOR = {Foata, Dominique and Han, Guo-Niu},
     TITLE = {A new proof of the {G}aroufalidis-{L}\^e-{Z}eilberger quantum
              {M}ac{M}ahon master theorem},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {307},
      YEAR = {2007},
    NUMBER = {1},
     PAGES = {424--431},
}

@article {FHMaster2,
    AUTHOR = {Foata, Dominique and Han, Guo-Niu},
     TITLE = {Specializations and extensions of the quantum {M}ac{M}ahon
              {M}aster {T}heorem},
   JOURNAL = {Linear Algebra Appl.},
  FJOURNAL = {Linear Algebra and its Applications},
    VOLUME = {423},
      YEAR = {2007},
    NUMBER = {2-3},
     PAGES = {445--455},
}
		
@article {FHMaster3,
    AUTHOR = {Foata, Dominique and Han, Guo-Niu},
     TITLE = {A basis for the right quantum algebra and the ``{$1=q$}''
              principle},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {27},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {163--172},
}		

@Article{FoSchut,
  author = 	 "D. Foata and M. P. {Sch\"utzenberger}",
  title = 	 "Major index and inversion number of permutations",
  journal =	 "Math. Nach.",
  year =	 1978,
  volume =	 83,
  pages =	 "143--159"
}

		  
@Article{FZDen,
  author = 	 "D. Foata and D. Zeilberger",
  title = 	 "Denert's permutation statistic is indeed {Euler-Mahonian}",
  journal =	 "Studies in Appl. Math.",
  year =	 1990,
  volume =	 83,
  pages =	 "31-59"
}

@article {FoZBab,
    AUTHOR = {Foata, Dominique and Zeilberger, Doron},
     TITLE = {Babson-{S}teingr\'\i msson statistics are indeed {M}ahonian
              (and sometimes even {E}uler-{M}ahonian)},
      NOTE = {Special issue in honor of Dominique Foata's 65th birthday
              (Philadelphia, PA, 2000)},
   JOURNAL = {Adv. in Appl. Math.},
  FJOURNAL = {Advances in Applied Mathematics},
    VOLUME = {27},
      YEAR = {2001},
    NUMBER = {2-3},
     PAGES = {390--404},
   MRCLASS = {60C05 (05A15 62G10)},
  MRNUMBER = {1868972 (2002i:60016)},
       DOI = {10.1006/aama.2001.0741},
       URL = {http://dx.doi.org/10.1006/aama.2001.0741},
}


@Article{FoZGraph1,
  author = 	 "D. Foata and D. Zeilberger",
  title = 	 "Graphical Major Indices",
  journal =	 "J. Comput. Applied Math",
  year =	 1996,
  volume =	 68,
  pages =	 "79--101"
}

		  
@Article{FoKrGraph2,
  author = 	 "D. Foata and C. Krattenthaler",
  title = 	 "Graphical Major Indices, {II}",
  journal =	 "S\'em. Lothar. Combin.",
  year =	 1995,
  volume =	 34,
  note =        {Art.\ B34k, approx.\ 16 pp.\ (electronic) }		  
}

@article {FockGonModuli,
    AUTHOR = {Fock, Vladimir and Goncharov, Alexander},
     TITLE = {Moduli spaces of local systems and higher {T}eichm\"uller
              theory},
   JOURNAL = {Publ. Math. Inst. Hautes \'Etudes Sci.},
  FJOURNAL = {Publications Math\'ematiques. Institut de Hautes \'Etudes
              Scientifiques},
    VOLUME = {103},
      YEAR = {2006},
     PAGES = {1--211},
}


@Article{FFLiPoon,
  author = 	 "S. Fomin and W. Fulton and C. K. Li and Y. Poon",
  title = 	 "Eigenvalues, singular values, and 
                  {Littlewood-Richardson} coefficients",
  journal =      "Amer. J. Math.",
  volume =       127,
  number =       1,
  pages =        "101--127",  
  year =	 2005
}


@Misc{FominComm,
  author = 	 "S. Fomin",
  year =         "2002",
  note = 	 "Personal communication"		  
}

@article {FominSTCComplex,
    AUTHOR = {Fomin, Sergey and Shapiro, Michael and Thurston, Dylan},
     TITLE = {Cluster algebras and triangulated surfaces. {I}. {C}luster
              complexes},
   JOURNAL = {Acta Math.},
  FJOURNAL = {Acta Mathematica},
    VOLUME = {201},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {83--146},
}

@Misc{FoZComm05,
  author = 	 "S. Fomin and A. Zelevinsky",
  year =         "2005",
  note = 	 "Personal communication"		  
}

@Misc{FoZComm07,
  author = 	 "S. Fomin and A. Zelevinsky",
  year =         "2007",
  note = 	 "Personal communication"		  
}
		  
@Article{FGNonComm,
  author = 	 "S. Fomin and C. Greene",
  title = 	 "Noncommutative {Schur} functions and their applications",
  journal =	 "Discrete Math.",
  year =	 1998,
  pages =        "179--200"
}


@Article{FominLoop,
  author = 	 "S. Fomin",
  title = 	 "Loop-erased walks and total positivity",
  journal =	 "Trans. Amer. Math. Soc..",
  year =	 2001,
  volume =       353,
  number =       9,
  pages =        "3563--3583"
}


@article {FominChap,
    AUTHOR = {Chapoton, Fr{\'e}d{\'e}ric and Fomin, Sergey and Zelevinsky,
              Andrei},
     TITLE = {Polytopal realizations of generalized associahedra},
      NOTE = {Dedicated to Robert V.\ Moody},
   JOURNAL = {Canad. Math. Bull.},
  FJOURNAL = {Canadian Mathematical Bulletin. Bulletin Canadien de
              Math\'ematiques},
    VOLUME = {45},
      YEAR = {2002},
    NUMBER = {4},
     PAGES = {537--566},
}

@Article{FK,
  author = 	 "S. Fomin and A. N. Kirillov",
  title = 	 "{Yang-Baxter Equation, Symmetric Functions,  and
		  Schubert Polynomials}",
  journal =	 "Proceedings of the Conference on Power Series and
		  Algebraic Combinatorics, Firenze",  
  year =	 1993
}


@Article{FK2,
  author = 	 "S. Fomin and A. N. Kirillov",
  title = 	 "{Combinatorial $B_{n}$ analogues of Schubert
		  polynomials}",
  journal =	 "Trans. Amer. Math. Soc.",
  volume =	 348,
  pages =	 {3591--3620},
  year =	 1996
}

		  
@Article{FK3,
  author = 	 "S. Fomin and A. N. Kirillov",
  title = 	 "Universal exponential solution of the {Yang-Baxter}
		  equation",
  journal =	 "Lett. Math. Phys.",
  year =	 1996,
  volume =	 37,
  number =	 3,
  pages =	 "273--284"
}


@Article{FK4,
  author = 	 "S. Fomin and A. N. Kirillov",
  title = 	 "Quadratic algebras, {D}unkl elements, 
                  and {S}chubert calculus",
  OPTcrossref =  "",
  journal =	 "Preprint",
  year =	 1997
}

@article {FominReading,
    AUTHOR = {Fomin, Sergey and Reading, Nathan},
     TITLE = {Generalized cluster complexes and {C}oxeter combinatorics},
   JOURNAL = {Int. Math. Res. Not.},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {2005},
    VOLUME = {44},
     PAGES = {2709--2757},
   MRCLASS = {05E15},
  MRNUMBER = {MR2181310 (2006g:05230)},
MRREVIEWER = {Axel Hultman},
}


@Article{FS,
  author = 	 "S. Fomin and R. P. Stanley",
  title = 	 "{Schubert Polynomials and the NilCoxeter Algebra}",
  journal =	 "Adv. Math.",
  year =	 1994,
  volume =	 103,
  pages =	 "196--207"
}

@Article{FominShapStrat,
  author = 	 "S. Fomin and M. Shapiro",
  title = 	 "Stratified spaces formed by totally positive varieties",
  journal =	 "Michigan Math. J.",
  year =	 2000,
  volume =	 48,
  pages =	 "253--270"
}

@article {FZCluster1,
    AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei},
     TITLE = {Cluster algebras. {I}. {F}oundations},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {15},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {497--529 (electronic)},
}

@article {FZCluster2,
    AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei},
     TITLE = {Cluster algebras. {II}. {F}inite type classification},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {154},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {63--121},
}
		
@article {FZCluster3,
    AUTHOR = {Berenstein, Arkady and Fomin, Sergey and Zelevinsky, Andrei},
     TITLE = {Cluster algebras. {III}. {U}pper bounds and double {B}ruhat
              cells},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {126},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {1--52},
}

@article {FZCluster4,
    AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei},
     TITLE = {Cluster algebras. {IV}. {C}oefficients},
   JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {143},
      YEAR = {2007},
    NUMBER = {1},
     PAGES = {112--164},
}
		
@article {FZLaurent,
    AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei},
     TITLE = {The {L}aurent phenomenon},
   JOURNAL = {Adv. in Appl. Math.},
  FJOURNAL = {Advances in Applied Mathematics},
    VOLUME = {28},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {119--144},
}

@Article{FominTPTest,
  author = 	 "Sergey Fomin and Andrei Zelevinsky",
  title = 	 "Total Positivity: Tests and Parametrizations",
  journal=	 "Math. Intelligencer",
  volume =       22,
  number =	 1,
  year =	 "2000",
  pages =	 "23--33",
       DOI = {10.1007/BF03024444},
       URL = {https://doi.org/10.1007/BF03024444},
}


@Article{FominDouble,
  author = 	 "Sergey Fomin and Andrei Zelevinsky",
  title = 	 "Double {Bruhat} Cells and Total Positivity",
  journal=	 "J. Amer. Math. Soc.",
  year =	 1999,
  volume =       12,
  pages =        "335--380"
}

@Article{FominParam,
  author = 	 "Sergey Fomin and Andrei Zelevinsky and Arkady Berenstein",
  title = 	 "Parametrizations of Canonical Bases and Totally Positive Matrices",
  journal=	 "Adv. Math.",
  year =	 1996,
  volume =       122,
  pages =        "49--149"
}

@Article{FominTNSemi,
  author = 	 "Sergey Fomin and Andrei Zelevinsky",
  title = 	 "Totally Nonnegative and Oscillatory Elements in Semisimple Groups",
  journal=	 "Proc. AMS",
  volume =       "128",
  pages =        "3749--3759",
  year =	 "2000"
}

@article {FZYSystems,
    AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei},
     TITLE = {{$Y$}-systems and generalized associahedra},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {158},
      YEAR = {2003},
    NUMBER = {3},
     PAGES = {977--1018},
}
		

@article {FFK,
    AUTHOR = {Frankl, Peter and F{\"u}redi, Zolt{\'a}n and Kalai, Gil},
     TITLE = {Shadows of colored complexes},
   JOURNAL = {Math. Scand.},
  FJOURNAL = {Mathematica Scandinavica},
    VOLUME = {63},
      YEAR = {1988},
    NUMBER = {2},
     PAGES = {169--178},
     CODEN = {MTSCAN},
   MRCLASS = {05A05 (06A07 52A40 55U99)},
  MRNUMBER = {MR1018807 (91b:05005)},
MRREVIEWER = {J. R. Griggs},
}


@article{FSSCrystal,
   AUTHOR = {Frappat, L and Sciarrino, A and Sorba, P},
    TITLE = {Crystalizing the genetic code},
  JOURNAL = {J. Biol. Phys.},
   VOLUME = {27},
     YEAR = {2001},
   NUMBER = {1},
    PAGES = {1--34}
}

@article {FKK,
    AUTHOR = {Frenkel, I. B. and Khovanov, M. G. and Kirillov, Jr., A. A.},
     TITLE = {Kazhdan-{L}usztig polynomials and canonical basis},
   JOURNAL = {Transform. Groups},
  FJOURNAL = {Transformation Groups},
    VOLUME = {3},
      YEAR = {1998},
    NUMBER = {4},
     PAGES = {321--336},
   MRCLASS = {20G05 (17B37 20C30)},
  MRNUMBER = {MR1657524 (2000f:20071)},
MRREVIEWER = {Andrzej Daszkiewicz},
}


@Book{FultonInter,
  author = 	 "W. Fulton",
  title = 	 "{Intersection Theory}",
  publisher = 	 "Springer-Verlag",
  year = 	 1984,
  address =	 "New York"
}
		  		  
@Article{Fulton1,
  author = 	 "W. Fulton",
  title = 	 "{Flags, Schubert polynomials, degeneracy loci, and
		  determinantal formulas}",
  journal =	 "Duke Math. J.",
  year =	 1991,
  volume =	 65,
  pages =	 "381--420"
}

		  		  
@Article{Fulton2,
  author = 	 "W. Fulton",
  title = 	 "{Determinantal Formulas for Orthogonal and Symplectic
		  Degeneracy Loci}",
  year =	 1996,
  journal =	 "J. Diff Geom."
}

@Article{Fulton3,
  author = 	 "W. Fulton",
  title = 	 "{Schubert varieties in flag bundles for
		  the classical groups}",
  journal =	 "Israel Math. Conf. Proc, Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry (Ramat Gan, 1993)",
   year =	 1996,
  volume =	 9,
  pages =	 "241-262"
 
}


@Misc{Fulton4,
  author = 	 "William Fulton",
  note = 	 "Personal communication",
  year =	 1994
}
		  
		  

@Article{Fulton5,
  author = 	  "William Fulton",
  title = 	 "Universal {Schubert} Polynomials",
  journal =	 "Preprint",
  year =	 1997,
  month =	 "Feb."
}

@Book{FultonYT,
  author = 	 "William Fulton",
  title = 	 "Young Tableaux; With Applications to Representation
		  Theory and Geometry",
  publisher = 	 "Cambridge University Press",
  year = 	 1997,
  volume =	 35,
  series =	 "London Mathematical Society Student Texts",
  address =	 "New York"
}

@article {GLZQMaster,
    AUTHOR = {Garoufalidis, Stavros and L{\^e}, Thang T. Q. and Zeilberger,
              Doron},
     TITLE = {The quantum {M}ac{M}ahon master theorem},
   JOURNAL = {Proc. Natl. Acad. Sci. USA},
  FJOURNAL = {Proceedings of the National Academy of Sciences of the United
              States of America},
    VOLUME = {103},
      YEAR = {2006},
    NUMBER = {38},
     PAGES = {13928--13931 (electronic)},
}

@Article{GallaiTrans,
  author = 	 "T. Gallai",
  title = 	 "Transitiv Orientierbare Graphen",
  journal =      "Acta. Math. Hungar.",
  year =	 1967,
  volume =       18,
  pages =        "25--66"

}

@Book{Gant0,
    AUTHOR = {Gantmacher, F. R.},
     TITLE = {Teoriya matric},
 PUBLISHER = {Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow},
      YEAR = {1953},
     PAGES = {491},
}
	  
@Book{Gant1,
  author = 	 "F. R. Gantmacher",
  title = 	 "{The Theory of Matrices}",
  publisher = 	 "Chelsea",
  year = 	 1959,
  volume =       1,		  
  address =	 "New York"
}

@Book{Gant2,
  author = 	 "F. R. Gantmacher",
  title = 	 "{The Theory of Matrices}",
  publisher = 	 "Chelsea",
  year = 	 1959,
  volume =       2,		  		  
  address =	 "New York"
}
		  
@Book{GantKreinOsz,
  author = 	 "F. R. Gantmacher and M. G. Krein",
  title = 	 "{Oszillationsmatrizen, Oszillationskerne und Kleine 
                 Schwingungen Mechanischer Systeme}",
  publisher = 	 "Akademie-Verlag",
  year = 	 1960,
  address =	 "Berlin"
}

@Book{GantKreinOsc,
  author = 	 "F. R. Gantmacher and M. G. Krein",
  title = 	 "Oscillation matrices and kernels and small
  vibrations of mechanical systems",
  publisher = 	 "AMS Chelsea Publishing",
  year = 	 2002,
  address =	 "Providence",
  note =         "Edited by A. Eremenko. Translation based on the 1941 Russian original."
}

@Book{G&J,
  author = 	 "M. Garey and D. Johnson",
  title = 	 "{Computers and Intractability: A Guide to the Theory
		  of $NP$-Completeness}",
  publisher = 	 "W. H. Freeman and Company",
  year = 	 1979,
  address =	 "New York"
}
		  
@Article{G&J75,
  author = 	 "M. Garey and D. Johnson",
  title = 	 "Complexity results for multiprocessor sceduling under
		  resource constraints",
  journal =      "SIAM J. Comput.",
  year =	 1975,
  volume =       4,
  pages =        "397--411"

}

@Article{GarGes,
  author = 	 "A. M. Garsia and I. Gessel",
  title = 	 "Permutation Statistics and Partitions",
  journal =      "Adv. Math.",
  year =	 1979,
  volume =       31,
  number =       3,
  pages =        "288--305"
}

@Article{GarMcL,
  author = 	 "A. M. Garsia and T. J. McLarnan",
  title = 	 "Relations between {Young's} natural and the {Kazhdan-Lusztig} representations of {$S_n$}", 
  journal =      "Adv. Math.",
  year =	 1988,
  volume =       69,
  pages =        "32-92"
}

@Article{GashInc,
  author = 	 "V. Gasharov",
  title = 	 "{Incomparability graphs of $(\mathbf{3+1})$-free posets are
                   $s$-positive}",
  journal =      "Discrete Math.",
  year =	 1996,
  volume =       157,
  pages =        "211-215"

}

@Article{GashNeg,
  author = 	 "V. Gasharov",
  title = 	 "{On the Neggers-Stanley conjecture and the Eulerian 
polynomials}",
  journal =      "J. Combin. Theory Ser. A",
  year =	 1998,
  volume =       82,
  number =       2,
  pages =        "134--146"

}
		  
		  
@Article{gasharov97,
  author = 	 "Vesselin Gasharov",
  title = 	 "Factoring the Poincar\'e polynomials for the Bruhat
order on $S_{n}$",
  journal =	 "In preparation",
  year =	 1997
}


@Article{Geck,
 author =        "M. Geck",
 title =         "Relative {Kazhdan}--{Lusztig} cells",
 journal =       "Representation Theory",
 volume =        10,
 year =          2006,
 pages =         "481--524"
}

@book{GPCharHecke,
    AUTHOR = {Geck, Meinolf and Pfeiffer, G{\"o}tz},
     TITLE = {Characters of finite {C}oxeter groups and {I}wahori--{H}ecke
              algebras},
    SERIES = {London Mathematical Society Monographs. New Series},
    VOLUME = {21},
 PUBLISHER = {The Clarendon Press Oxford University Press},
   ADDRESS = {New York},
      YEAR = {2000},
     PAGES = {xvi+446},
}
		
@article {GSVClusterPoisson,
    AUTHOR = {Gekhtman, Michael and Shapiro, Michael and Vainshtein, Alek},
     TITLE = {Cluster algebras and {P}oisson geometry},
      NOTE = {\{Dedicated to Vladimir Igorevich Arnold on the occasion of
              his 65th birthday\}},
   JOURNAL = {Mosc. Math. J.},
  FJOURNAL = {Moscow Mathematical Journal},
    VOLUME = {3},
      YEAR = {2003},
    NUMBER = {3},
     PAGES = {899--934, 1199},
}

@article{GSBoundedRatios,
    AUTHOR = {Soskin, Daniel and Gekhtman, Michael},
     TITLE = {On bounded ratios of minors of totally positive matrices},
   JOURNAL = {Linear Algebra Appl.},
  FJOURNAL = {Linear Algebra and its Applications},
    VOLUME = {715},
      YEAR = {2025},
     PAGES = {46--67}, 
       DOI = {10.1016/j.laa.2025.03.013},
       URL = {https://doi.org/10.1016/j.laa.2025.03.013},
}

@Inproceedings{GelZelCan,
  author = 	 "I. Gelfand and A. Zelevinsky",
  title = 	 "Canonical basis in irreducible representations of $gl_3$ 
                  and its applications", 
  year =	 1986,
  booktitle =    "Group Theoretical Methods in Physics, Vol. II (Jurmala, 1985)", 
  publisher =    "VNU Sci. Press",
  address =      "Utrecht",
  pages =	 "127--146"
}		  

@incollection {GIRRNuke,
    AUTHOR = {Georgieva, A. and Ivanov, M. and Raychev, P. and Roussev, R.},
     TITLE = {Boson representation of {${\rm Sp}(24,{\bf R})$} and
              classification of even-even nuclei},
 BOOKTITLE = {Group theoretical methods in physics (Varna, 1987)},
    SERIES = {Lecture Notes in Phys},
    VOLUME = {313},
     PAGES = {408--413},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1988},
   MRCLASS = {81G30},
  MRNUMBER = {MR977328 (89k:81196)},
}

@article {GerstenDeform,
    AUTHOR = {Gerstenhaber, Murray},
     TITLE = {On the deformation of rings and algebras},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {79},
      YEAR = {1964},
     PAGES = {59--103},
   MRCLASS = {16.90 (13.93)},
  MRNUMBER = {MR0171807 (30 \#2034)},
MRREVIEWER = {D. Zelinsky},
}

@PhdThesis{GesThesis,
  author = 	 "I. Gessel",
  title = 	 "Generating functions and enumeration of sequences",
  school = 	 "MIT",
  year = 	 1977,
  address =	 "Cambridge, MA"
}

@Misc{GesComm,
  author = 	 "I. Gessel",
  year =         "1999",
  note = 	 "Personal communication"
}

@Unpublished{GV,
  author = 	 "I. Gessel and G. Viennot",
  title = 	 "Determinants and plane partitions",
  note =	 "Preprint",
  year =	 1989
}

@article{GVBin,
  author = 	 "I. Gessel and G. Viennot",
  title = 	 "Binomial Determinants, Paths, and Hook Length Formulae",
  journal =	 "Adv. Math.",
  year =	 1985,
  number =       3,		  
  pages =        "300-321",
  volume =       58
}

		  
@Book{GHJ,
  author = 	 "F. M. Goodman and P. de la Harpe and V.F.R. Jones",
  title = 	 "{Coxeter  Graphs  and  Towers  of Algebras}",
  publisher = 	 "Springer--Verlag",
  year = 	 1989,
  address =	 "New York"
}

		  
@Article{GJFormal1,
  author = 	 "D. M. Jackson and I. P. Goulden",
  title = 	 "A Formal Calculus for the Enumerative System of
		  Sequences - {I}. Combinatorial Theorems",
  journal =	 "Studies in Applied Mathematics",
  year =	 1979,
  pages =        "141--178",
  volume =       61
}


@Article{GJImm,
  author = 	 "I. P. Goulden and D. M. Jackson",
  title = 	 "Immanants of combinatorial matrices",
  journal =	 "J. Algebra",
  year =	 1992,
  pages =        "305--324",
  volume =       148
}

@article{GJMaster,
    AUTHOR = {Goulden, I. P. and Jackson, D. M.},
     TITLE = {Immanants, {S}chur functions, and the {M}ac{M}ahon master
              theorem},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {115},
      YEAR = {1992},
    NUMBER = {3},
     PAGES = {605--612},
}
		

@Article{GKM,
  author = 	 "M. Goresky and R.Kottwitz and R. MacPherson",
  title = 	 "Equivariant cohomology {Koszul} duality, and the
		  localization theorem",
  journal =	 "preprint",
  year =	 1996
}


@Article{g-m,
  author = 	 "M. Goresky and R. MacPherson",
  title = 	 "Intersection Homology-II",
  journal =	 "Invent. Math.",
  volume =	 71,
  pages =	 "77--129",		  
  year =	 1983
}		  

		  
@Article{graham,
  author = 	 {William Graham},
  title = 	 {The class of the diagonal in flag bundles},
  journal = 	 {preprint},
  year = 	 1997
}

@Article{GreeneRSK,
 author =        "C. Greene",
 title =         "An extension of {Schensted's} theorem",
 journal =       "Adv. Math",
 year =          1974,
 pages =         "104--109",
 volume =        14
}

@Article{GreeneImm,
  author = 	 "C. Greene",
  title = 	 "Proof of a conjecture on immanants of the 
                 {Jacobi-Trudi} matrix",
  journal =	 "Linear Algebra Appl.",
  year =	 1992,
  volume =	 171,
  pages =	 "65--79"
}


@Incollection{GreeneKleit,
  author = 	 "C. Greene and D. Kleitman",
  title = 	 "Proof techniques in the theory of finite sets",
  editor =       "G. C. Rota",
  year =	 1978,
  booktitle =    "Studies in Combinatorics",
  publisher =    "Mathematical Association of America",
  pages =	 "22-79"
}		
  
@Unpublished{GKLSXIneqSF3,
  author = 	 "C. Greene and J. Kroll and J. Lima and M. Skandera and R. Xu",
  title = 	 "Inequalities for Symmetric Functions of Degree $3$",
  year =	 2009,
  note =         "In preparation"
}

@incollection {GrojLusBIRQ,
    AUTHOR = {Grojnowski, I. and Lusztig, G.},
     TITLE = {On bases of irreducible representations of quantum {${\rm
              GL}\sb n$}},
 BOOKTITLE = {Kazhdan-Lusztig theory and related topics (Chicago, IL, 1989)},
    SERIES = {Contemp. Math},
    VOLUME = {139},
     PAGES = {167--174},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1992},
}
	
@Unpublished{GPModRel,
  author = 	 "Matthieu Guay-Paquet",
  title = 	 "A modular relation for the chromatic symmetric functions of $(\mathbf 3 + \mathbf 1 )$-free posets",
  note =         "Preprint {\tt math.CO/1306.2400} on {ArXiv}",
  year =	 2013
}

@Unpublished{GPSecondPf,
  author = 	 "Matthieu Guay-Paquet",
  title = 	 "A second proof of the {Shareshian}--{Wachs} conjecture, by way of a new {Hopf} algebra",
  note =         "Preprint {\tt math.CO/1601.05498} on {ArXiv}",
  year =	 2016
}

@InCollection{HagOWRook,
  author = 	 "J. Haglund and K. Ono and D. Wagner",
  title = 	 "Theorems and Conjectures involving rook polynomials
		  with only real zeros",
  booktitle =	 "Topics in Number Theory",
  editor =	 "S. D. Ahlgren",
  journal =	 "Adv. Math.",
  publisher =    "Kluwer",
  year =	 1999,
  pages =	 "207--221"
}
		  
@Article{HagFurther,
  author = 	 "J. Haglund",
  title = 	 "Further Investigations involving rook polynomials
		  with only real roots",
  journal =	 "Europ. J. Combin.",
  year =	 2000,
  volume =	 21,
  pages =	 "1017--1037"
}

@book {Hagqt,
    AUTHOR = {Haglund, James},
     TITLE = {The {$q$},{$t$}-{C}atalan numbers and the space of diagonal
              harmonics},
    SERIES = {University Lecture Series},
    VOLUME = {41},
      NOTE = {With an appendix on the combinatorics of Macdonald
              polynomials},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2008},
     PAGES = {viii+167},
      ISBN = {978-0-8218-4411-3; 0-8218-4411-3},
   MRCLASS = {05E05 (05A05 05A30 33D52)},
  MRNUMBER = {2371044},
MRREVIEWER = {Michael A. Zabrocki},
       DOI = {10.1007/s10711-008-9270-0},
       URL = {https://doi.org/10.1007/s10711-008-9270-0},
}

@article {HaiLorenzKqMM,
    AUTHOR = {Hai, Ph{\`u}ng H{\^o} and Lorenz, Martin},
     TITLE = {Koszul algebras and the quantum {M}ac{M}ahon master theorem},
   JOURNAL = {Bull. Lond. Math. Soc.},
  FJOURNAL = {Bulletin of the London Mathematical Society},
    VOLUME = {39},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {667--676},
}
		  
@Article{Haiman,
  author = 	 "M. Haiman",
  title = 	 "{Dual equivalence with applications, including a
		  conjecture of Proctor}",
  journal =	 "Discrete Math.",
  year =	 1992,
  volume =	 99,
  pages =	 "79--113"
}

@Article{HaimanHecke,
  author = 	 "M. Haiman",
  title = 	 "Hecke algebra characters and immanant conjectures",
  journal =	 "J. Amer. Math. Soc.",
  year =	 1993,
  volume =	 6,
  number =       3,
  pages =	 "569--595"
}

@Unpublished{HaimanEnumSmooth,
  author = 	 "M. Haiman",
  title = 	 "Enumeration of smooth {Schubert} varieties",
  note = 	 "Preprint",
  year =	 2004
}

@article {HRam96,
    AUTHOR = {Halverson, Tom and Ram, Arun},
     TITLE = {Murnaghan-{N}akayama rules for characters of {I}wahori-{H}ecke
              algebras of classical type},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {348},
      YEAR = {1996},
    NUMBER = {10},
     PAGES = {3967--3995},
   MRCLASS = {20C15},
  MRNUMBER = {1322951},
MRREVIEWER = {Fran\c{c}ois Digne},
       DOI = {10.1090/S0002-9947-96-01491-2},
       URL = {https://doi.org/10.1090/S0002-9947-96-01491-2},
}

@Article{HPHowOften,
  author = 	 "A. Hammet and Boris Pittel",
  title = 	 "How often are two permutations comparable?",
  year =	 2008,
  journal =	 "Trans. Amer. Math. Soc.",
  volume =	 360,
  number =       9,
  pages =	 "4541--4568"
}

		  
@Article{HanDen,
  author = 	 "G. N. Han",
  title = 	 "Une transformation fondamentale sur les r\'earrangements
                 de mots",
  journal =	 "Adv. Math.",
  year =	 1994,
  volume =	 105,
  pages =	 "26--41"
}

@Article{HanEMTriple,
  author = 	 "G. N. Han",
  title = 	 "{Euler-Mahonien} triple set-valued statistics on permutations",
  journal =	 "European J. Combin.",
  year =	 2008,
  volume =	 29,
  number =       3,
  pages =	 "568--580"
}


@article {HPCohAbe,
    AUTHOR = {Harada, Megumi and Precup, Martha},
     TITLE = {The cohomology of abelian {Hessenberg} varieties and the {Stanley-Stembridge} conjecture},
   JOURNAL = {Algebraic Combinatorics},
  FJOURNAL = {Algebraic Combinatorics},
    VOLUME = {2},
      YEAR = {2019},
    NUMBER = {6},
     PAGES = {1059--1108},
}

@article{HPTPermutationBases,
  author = 	 "Harada, Megumi and Precup, Martha and Tymoczko, Juliana",
  title = 	 "Toward permutation bases in the equivariant cohomology rings of regular semisimple {Hessenberg} varieties",
  journal =	 "La Matematica",
  year =	 2021,
  volume =       1,
  pages =        "263--316",
}

@Unpublished{HPTPermutationBasesArx,
  author = 	 "Megumi Harada and Martha Precup and Juliana Tymoczko ",
  title = 	 "Permutation bases in the equivariant cohomology rings of regular semisimple {Hessenberg} varieties",
  note =         "Preprint {\tt math.CO/2101.03191} on {ArXiv}",
  year =	 2021
}

@article {HararyNBSG,
    AUTHOR = {Harary, Frank},
     TITLE = {On the notion of balance of a signed graph},
   JOURNAL = {Michigan Math J.},
    VOLUME = {2},
      YEAR = {1953/1954},
    NUMBER = {2},
     PAGES = {143--146},
}




@Book{HardyIneq,
  author = 	 "G. H. Hardy and J. E. Littlewood and G. {P\'olya}",
  title = 	 "Inequalities",
  publisher = 	 "Cambridge University Press",
  year = 	 1934,
  address =	 "Cambridge"
}

@book {Harris,
    AUTHOR = {Harris, Joe},
     TITLE = {Algebraic geometry},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {133},
      NOTE = {A first course},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1992},
     PAGES = {xx+328},
   MRCLASS = {14-01},
  MRNUMBER = {MR1182558 (93j:14001)},
MRREVIEWER = {Liam O'Carroll},
}

@book {Hartshorne,
    AUTHOR = {Hartshorne, Robin},
     TITLE = {Algebraic geometry},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {52},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1977},
     PAGES = {xvi+496},
   MRCLASS = {14-01},
  MRNUMBER = {MR0463157 (57 \#3116)},
MRREVIEWER = {Robert Speiser},
}

@article {HayashiCGroups,
    AUTHOR = {Hayashi, Takahiro},
     TITLE = {Quantum deformation of classical groups},
   JOURNAL = {Publ. Res. Inst. Math. Sci.},
  FJOURNAL = {Kyoto University. Research Institute for Mathematical
              Sciences. Publications},
    VOLUME = {28},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {57--81},
   MRCLASS = {17B37 (16W30)},
  MRNUMBER = {1147851},
MRREVIEWER = {Dmitri\u{\i} I. Gurevich},
       DOI = {10.2977/prims/1195168856},
       URL = {https://doi.org/10.2977/prims/1195168856},
}

@article {HayashiDet,
    AUTHOR = {Hayashi, Takahiro},
     TITLE = {Quantum groups and quantum determinants},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {152},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {146--165},
   MRCLASS = {17B37 (16W30)},
  MRNUMBER = {1190409},
MRREVIEWER = {Marco Tarlini},
       DOI = {10.1016/0021-8693(92)90093-2},
       URL = {https://doi.org/10.1016/0021-8693(92)90093-2},
}
		

@Article{HeilLieb,
  author = 	 "O. Heilman and E. Lieb",
  title = 	 "Theory of monomer-dimer systems",
  journal =	 "Comm. Math. Physics",
  pages =        "190-232",
  volume =       25,
  year =	 1972		  
}

@Article{HetyeiCentral,
  author = 	 "G\'abor Hetyei",
  title = 	 "Central {Delanoy} numbers and balanced {Cohen-Macaulay}
complexes",
  year =	 2006,
  journal =	 "Ann. Comb.",
  volume =	 10,
  number =       4,
  pages =	 "443--462"
}
		  
@Article{HeyfronImmDom,
  author = 	 "P. Heyfron",
  title = 	 "Immanant dominance orderings for hook partitions",
  journal =	 "Linear and Multilinear Algebra",
  pages =        "65--78",
  volume =       24,
  number =       1,
  year =	 1988		  
}

		  
@Article{HibiLinear,
  author = 	 "T. Hibi",
  title = 	 "Linear and nonlinear inequalities concerning a certain combinatorial sequence which arises from counting the number of chains of a finite distributive lattice",
  journal =	 "Discrete Appl. Math.",
  year =	 1991,
  volume =	 34,
  pages =	 "145--150"
}

@Article{HibiWhat,
  author = 	 "T. Hibi",
  title = 	 "What can be said about pure ${O}$-sequences?",
  journal =	 "J. Combin. Theory Ser. A",
  year =	 1989,
  volume =	 50,
  pages =	 "319--322"
}

@Book{Hiller,
  author = 	 "H. Hiller",
  title = 	 "{Geometry of Coxeter Groups}",
  publisher = 	 "Pitman Advanced Publishing Program",
  year = 	 1982
}

@Article{HB,
  author = 	 "H. Hiller and B.Boe",
  title = 	 "{Pieri formula for $SO_{2n+1}/U_{n}$ and $Sp_{n}/U_{n}$}",
  year =	 1986,
  journal =	 "Adv. Math.",
  volume =	 62,
  pages =	 "49--67"
}

@Book{Hirz,
  author = 	 "F. Hirzebrusch",
  title = 	 "{Topological methods in Algebraic Geometry}",
  publisher = 	 "Spriger-Verlag",
  year = 	 1978
}


@Unpublished{Hoch266,
  author = 	 "D. Hochbaum",
  title = 	 "{Graph Algorithms and Network Flows}",
  note = 	 "Course Notes from IEOR 266, UC-Berkeley",
  year =	 1997,
  month =	 "Spring"
}

@PhdThesis{HoefsmitThesis,
    AUTHOR = {Hoefsmit, Peter Norbert},
     TITLE = {Representations of Hecke algebras of finite groups with BN-pairs of classical type},
    SCHOOL = {University of British Columbia},
 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {1974},
     PAGES = {(no paging)},
   address = {Vancouver, BC, Canada},
   MRCLASS = {Thesis},
  MRNUMBER = {2624950},
       URL =
              {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:NK22107},
}


@misc{HoSkanDoubleCoset,
    AUTHOR = {C. Hohlweg and M. Skandera},
EPRINT = {0511611},
EPRINTTYPE = {arxiv},
     TITLE = {A note on {B}ruhat order and double coset representatives},
      YEAR = {2005}
}

@article{HZStandard,
    AUTHOR = {Huang, Rosa Q. and Zhang, James J.},
     TITLE = {Standard basis theorem for quantum linear groups},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {102},
      YEAR = {1993},
    NUMBER = {2},
     PAGES = {202--229},
     CODEN = {ADMTA4},
   MRCLASS = {16W30 (05E10 17B37)},
  MRNUMBER = {MR1252032 (94j:16067)},
MRREVIEWER = {E. J. Taft},
}
		  
@Book{Hum,
  author = 	 "James E. Humphreys",
  title = 	 "{Reflection groups and Coxeter groups}",
  publisher = 	 "Cambridge University Press",
  year = 	 1990
}

@Book{Hum2,
  author = 	 "James E. Humphreys",
  title = 	 "{Introduction to Lie Algebras and Representation Theory}",
  publisher = 	 "Springer-Verlag",
  year = 	 1972,
  number =	 9,
  series =	 "GTM",
  address =	 "New York"
}


@Book{Hum-LAG,
  author = 	  "James E. Humphreys",
  title = 	 "Linear Algebraic Groups",
  publisher = 	 "Springer-Verlag",
  year = 	 1975,
  volume =	 21,
  series =	 "Graduate texts in mathematics",
  address =	 "New York",

}

@unpublished{HusainTNN,
  author = 	 "S. Ali Husain",
  title = 	 "Totally nonnegative polynomials",
  year =	 2004,
  note =         "unpublished REU paper"
}

@article {IrvingSocle,
    AUTHOR = {Irving, Ronald S.},
     TITLE = {The socle filtration of a {V}erma module},
   JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
  FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
              Quatri\`eme S\'erie},
    VOLUME = {21},
      YEAR = {1988},
    NUMBER = {1},
     PAGES = {47--65},
     CODEN = {ASENAH},
   MRCLASS = {17B35},
  MRNUMBER = {MR944101 (89h:17015)},
MRREVIEWER = {Anthony Joseph},
}

@article {IwahoriHecke,
    AUTHOR = {Iwahori, Nagayoshi},
     TITLE = {On the structure of a {H}ecke ring of a {C}hevalley group over
              a finite field},
   JOURNAL = {J. Fac. Sci. Univ. Tokyo Sect. I},
  FJOURNAL = {Journal of the Faculty of Science. University of Tokyo.
              Section I},
    VOLUME = {10},
      YEAR = {1964},
     PAGES = {215--236},
   MRCLASS = {20.75 (20.80)},
  MRNUMBER = {165016},
MRREVIEWER = {Rimhak\ Ree},
}

@Article{JamesImm,
  author = 	 "G. James",
  title = 	 "Immanants",
  year =	 1992,
  journal =	 "Linear and Multilinear Algebra",
  volume =	 32,
  pages =	 "197--210"
}

@book{JK,
    AUTHOR = {James, Gordon and Kerber, Adalbert},
     TITLE = {The representation theory of the symmetric group},
    SERIES = {Encyclopedia of Mathematics and its Applications},
    VOLUME = {16},
 PUBLISHER = {Addison-Wesley Publishing Co., Reading, Mass.},
      YEAR = {1981},
}


@article {JimboqDYBE,
    AUTHOR = {Jimbo, Michio},
     TITLE = {A {$q$}-difference analogue of {$U(\mathfrak{g})$} and
              the {Y}ang-{B}axter equation},
   JOURNAL = {Lett. Math. Phys.},
  FJOURNAL = {Letters in Mathematical Physics. A Journal for the Rapid
              Dissemination of Short Contributions in the Field of
              Mathematical Physics},
    VOLUME = 10,
      YEAR = 1985,
    NUMBER = 1,
     PAGES = {63--69},
}

@article {JimboqHYB,
    AUTHOR = {Jimbo, Michio},
     TITLE = {A {$q$}-analogue of {$U(\mathfrak{gl}(N+1))$}, {H}ecke
              algebra, and the {Y}ang-{B}axter equation},
   JOURNAL = {Lett. Math. Phys.},
  FJOURNAL = {Letters in Mathematical Physics. A Journal for the Rapid
              Dissemination of Short Contributions in the Field of
              Mathematical Physics},
    VOLUME = {11},
      YEAR = {1986},
    NUMBER = {3},
     PAGES = {247--252},
     CODEN = {LMPDHQ},
   MRCLASS = {17B25 (58F07 82A15)},
  MRNUMBER = {MR841713 (87k:17011)},
MRREVIEWER = {Nick Yu. Reshetikhin},
}


@incollection {JohnSachsCalc,
    AUTHOR = {John, Peter and Sachs, Horst},
     TITLE = {Calculating the number of perfect matchings and {P}auling's
              bond orders in hexagonal systems whose inner dual is a tree},
 BOOKTITLE = {Graphs, hypergraphs and applications (Eyba, 1984)},
    SERIES = {Teubner-Texte Math},
    VOLUME = {73},
     PAGES = {80--91},
 PUBLISHER = {Teubner},
   ADDRESS = {Leipzig},
      YEAR = {1985},
   MRCLASS = {92A40 (05A15 05C70)},
  MRNUMBER = {MR869443 (87m:92103)},
}


@article {JNTP2,
    AUTHOR = {Johnson, C. R. and Nasserasr, S.},
     TITLE = {{${\rm TP}_2={\rm Bruhat}$}},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {310},
      YEAR = {2010},
    NUMBER = {10-11},
     PAGES = {1627--1628},
     CODEN = {DSMHA4},
   MRCLASS = {05A05},
  MRNUMBER = {2601272 (2011e:05010)},
       DOI = {10.1016/j.disc.2009.12.021},
       URL = {http://dx.doi.org/10.1016/j.disc.2009.12.021},
}

@Book{Kac,
  author = 	 "Victor G. Kac",
  title = 	 "Infinite Dimensional Lie Algebras",
  publisher = 	 "Cambridge University Press",
  year = 	 1990,
  edition =	 "Third"
}


@Incollection{KalaiDiam,
  author = 	 "G. Kalai",
  title = 	 "The Diameter of Graphs of Convex Polytopes and
		  $f$-Vector Theory",
  year =	 1991,
  booktitle =    "DIMACS Ser. Disc. Math. Theoret. Comput. Sci.",
  volume =       4,		  
  publisher =    "American Mathematical Society",
  pages =	 "387-411"
}		  
		  
@Unpublished{KaliHookunpub,
  author = 	 "Ryan Kaliszewski",
  title = 	 "Hook coefficients of chromatic functions",
  note =         "Preprint {\tt math.CO/1404.7531} on {ArXiv}",
  year =	 2014
}

@article{KaliHook,
    AUTHOR = {Kaliszewski, Ryan},
     TITLE = {Hook coefficients of chromatic functions},
   JOURNAL = {J. Comb.},
  FJOURNAL = {Journal of Combinatorics},
    VOLUME = {6},
      YEAR = {2015},
    NUMBER = {3},
     PAGES = {327--337},
   MRCLASS = {05C31 (05C15 05E05)},
  MRNUMBER = {3357127},
MRREVIEWER = {Julian Dodji Allagan},
       DOI = {10.4310/JOC.2015.v6.n3.a4},
       URL = {https://doi.org/10.4310/JOC.2015.v6.n3.a4},
}

@Unpublished{KLSBasesQMBIndSgnunpub,
  author = 	 "Ryan Kaliszewski and Justin Lambright and Mark Skandera",
  title = 	 "Bases of the quantum matrix bialgebra and induced sign characters of the {Hecke} algebra",
  note =         "Preprint {\tt math.CO/1802.04856} on {ArXiv}, to appear in {\em J.\ Algebr.\ Comb.}",
  year =	 2018
}

@article {KLSBasesQMBIndSgn,
    AUTHOR = {Kaliszewski, Ryan and Lambright, Justin and Skandera, Mark},
     TITLE = {Bases of the quantum matrix bialgebra and induced sign
              characters of the {H}ecke algebra},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {49},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {475--505},
   MRCLASS = {20C08 (15A15)},
  MRNUMBER = {3954432},
       DOI = {10.1007/s10801-018-0832-4},
       URL = {https://doi.org/10.1007/s10801-018-0832-4},
}

@Book{KarlinGame,
  author = 	 "S. Karlin",
  title = 	 "Mathematical methods and theory in games, programming, and
  economics",
  publisher = 	 "Addison-Wesley",
  year = 	 1959,
  address =      "Reading, MA"
}

			  
@Article{KMG,
  author = 	 "S. Karlin and G. {McGregor}",
  title = 	 "Coincidence probabilities",
  journal =	 "Pacific J. Math.",
  year =	 1959,
  volume =	 9,
  pages =	 "1141--1164"
}		  

@Article{KarlinRinott,
  author = 	 "S. Karlin and Y. Rinott",
  title = 	 "A generalized {Cauchy-Binet} formula and applications 
                  to total positivity and majorization", 
  journal =	 "J. Multivariate Anal.",
  year =	 1988,
  volume =	 27,
  pages =	 "284--299"
}		  
		  
@article{KashCrystal,
  author =   {M. Kashiwara},
  title =    {On crystal bases of the {$Q$}-analog of universal enveloping algebras},
  journal =  {Duke Math. J.},
  year =     {1991},
  volume =   {63},
  pages =    {465--516},
}


@article {KashGlobal,
    AUTHOR = {Kashiwara, Masaki},
     TITLE = {Global crystal bases of quantum groups},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {69},
      YEAR = {1993},
    NUMBER = {2},
     PAGES = {455--485},
       URL = {http://dx.doi.org/10.1215/S0012-7094-93-06920-7},
}
		
@Incollection{KatonaThm,
  author = 	 "G. Katona",
  title = 	 "A theorem of finite sets",
  booktitle =    "Colloquium on the Theory of Graphs", 
  publisher =    "Academic Press and Akademiai Kiad\'o",
  address =      "New York and Budapest",		  
  year =	 "1968",
  pages =        "187--207"
}


@Article{KauffState,
  author = 	 "L. Kauffman",
  title = 	 "State models and the {Jones} polynomial",
  journal =	 "Topology",
  year =	 1987,
  volume =	 26,
  number =       3,
  pages =	 "395--407"
}		  

@article {KauffKnotPhysics,
    AUTHOR = {Kauffman, L. H.},
     TITLE = {Knots and physics},
      NOTE = {Conference on Differential Geometry and Topology (Italian)
              (Lecce, 1989)},
   JOURNAL = {Note Mat.},
  FJOURNAL = {Note di Matematica},
    VOLUME = {9},
      YEAR = {1989},
    NUMBER = {suppl.},
     PAGES = {17--32},
   MRCLASS = {57M25 (17B37 82B23)},
  MRNUMBER = {MR1154129 (93a:57009)},
MRREVIEWER = {Yongwu Rong},
}
		  
@Article{KLRepCH,
    AUTHOR = {Kazhdan, David and Lusztig, George},
     TITLE = {Representations of {C}oxeter groups and {H}ecke algebras},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {53},
      YEAR = {1979},
    NUMBER = {2},
     PAGES = {165--184},
       DOI = {10.1007/BF01390031},
       URL = {https://doi.org/10.1007/BF01390031},
}
		  

@Article{KLSchub,
  author = 	 "D. Kazhdan and G. Lusztig",
  title = 	 "{Schubert varieties and Poincar\'e duality}",
  journal =	 "Proc. Symp. Pure. Math., A.M.S.",
  year =	 1980,
  volume =	 36,
  pages =	 "185-203"
}		  

@Incollection{KellyTrotter,
  author = 	 "D. Kelly and W. T. Trotter",
  title = 	 "Dimension theory for partially ordered sets",
  editor =       "I. Rival",
  year =	 1981,
  booktitle =    "Ordered Sets",
  publisher =    "D. Reidel Publishing Company",
  address =      "Dordrecht-Holland",
  pages =	 "171--212"
}
		  		  
@Book{KR,
  author = 	 "Brian W. Kernighan and Dennis M. Ritchie",
  title = 	 "The C Programming Language",
  publisher = 	 "Prentice Hall",
  year = 	 1988,
  edition =	 "2nd"
}

@incollection {KerVerCFR,
    AUTHOR = {Kerov, S. V. and Vershik, A. M.},
     TITLE = {Characters, factor representations and {$K$}-functor of the
              infinite symmetric group},
 BOOKTITLE = {Operator algebras and group representations, {V}ol. {II}
              ({N}eptun, 1980)},
    SERIES = {Monogr. Stud. Math.},
    VOLUME = {18},
     PAGES = {23--32},
 PUBLISHER = {Pitman},
   ADDRESS = {Boston, MA},
      YEAR = {1984},
   MRCLASS = {22D10 (16A54 20C32 22D40 46L80 46M20)},
  MRNUMBER = {733300 (86a:22006)},
MRREVIEWER = {E. Thoma},
}

@article {KingWRepTr,
    AUTHOR = {King, R. C. and Wybourne, B. G.},
     TITLE = {Representations and traces of the {H}ecke algebras {$H\sb
              n(q)$} of type {$A\sb {n-1}$}},
   JOURNAL = {J. Math. Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {33},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {4--14},
}
		  
@Article{KL,
  author = 	 "S. L. Kleiman and D. Laksov",
  title = 	 "{Schubert calculus}",
  journal =	 "Amer.\ Math.\ Monthly",
  year =	 1972,
  volume =	 79,
  pages =	 "1061--1082"
}

@Proceedings{Kleiman,
  author = 	 "S. L. Kleiman",
  title = 	 "{Problem 15.  Rigorous foundation of Schubert's
		  enumerative calculus}",
  pages =	 "445--482",
  year =	 1976,
  volume =	 28,
  publisher =	 "Amer. Math. Soc.",
  organization = "In Mathematical Developments Arising from Hilbert
		  Problems, Proceedings of Symposia in Pure Mathematics", 
  address =	 "Providence, R.I."
}

@Article{KleitRoth,
  author = 	 "D. Kleitman and B. Rothschild",
  title = 	 "The number of finite topologies",
  journal =	 "Proc. Amer. Math. Soc.",
  year =	 1970,
  volume =	 25,
  pages =	 "276--282"
}

@Article{K,
  author = 	 "A. Kohnert",
  title = 	 "{Weintrauben, Polynome, Tableaux}",
  journal =	 "Bayreuther Math",
  year =	 1990,
  volume =	 38,
  pages =	 "1--97"
}

@Book{Knuth3,
  author = 	 "D. E. Knuth",
  title = 	 "{The Art of Computer Programming}",
  publisher = 	 "Addison--Wesley",
  year = 	 1973,
  volume =	 3,
  address =	 "Reading, MA"
}

@Article{KonPakMaster,
  author = 	 "M. Konvalinka and I. Pak",
  title = 	 "Non-commutative extensions of the {MacMahon} Master Theorem",
  journal =	 "Adv. Math.",
  volume =       215,
  number =       1,
  year =	 2007,
  pages =	 "29--61"
}

@article {KSkanQGJ,
    AUTHOR = {Konvalinka, Matja{\v{z}} and Skandera, Mark},
     TITLE = {Generating functions for {H}ecke algebra characters},
   JOURNAL = {Canad.\ J.\ Math.},
  FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de
              Math\'ematiques},
    VOLUME = {63},
      YEAR = {2011},
    NUMBER = {2},
     PAGES = {413--435},
}


@Misc{KostComm,
  author = 	 "Bertram Kostant",
  year =         "2000",
  note = 	 "Personal communication"
}

@Article{Kostant59,
  author = 	 {Bertram Kostant},
  title = 	 {The Principal Three-Dimensional Subgroup and the Betti numbers of a Complex Simple Lie Group},
  journal = 	 {Amer. J. Maths.},
  year = 	 1959,
  volume =	 81,
  pages =	 {973-1032}
}

@Article{KK,
  author = 	 "Bertram Kostant and Shrawan Kumar",
  title = 	 "{The Nil Hecke Ring and Cohomology of $G/P$ for a
		  Kac-Moody Group $G^*$}",
  journal =	 "Adv. Math.",
  year =	 1986,
  volume =	 62,
  pages =	 "187-237"
}

@incollection {KostantGoverZ,
    AUTHOR = {Kostant, Bertram},
     TITLE = {Groups over {$Z$}},
 BOOKTITLE = {Algebraic {G}roups and {D}iscontinuous {S}ubgroups ({P}roc.
              {S}ympos. {P}ure {M}ath., {B}oulder, {C}olo., 1965)},
     PAGES = {90--98},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, R.I.},
      YEAR = {1966},
MRREVIEWER = {A. Borel},
}


@Article{KostantImm,
  author = 	 "Bertram Kostant",
  title = 	 "Immanant inequalities and {$0$}-weight spaces",
  journal =	 "J. Amer. Math. Soc.",
  year =	 1995,
  volume =	 8,
  number =       1,
  pages =	 "181--186"
}

@article {KotelPropRuss,
    AUTHOR = {Kotelyanski\u{\i}, D. M.},
     TITLE = {On a property of sign-symmetric matrices},
   JOURNAL = {Uspehi Matem. Nauk (N.S.)},
  FJOURNAL = {Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo.
              Uspekhi Matematicheskikh Nauk},
    VOLUME = {8},
      YEAR = {1953},
    NUMBER = {4(56)},
     PAGES = {163--167},
   MRCLASS = {09.0X},
  MRNUMBER = {0057212},
MRREVIEWER = {J. L. Brenner},
}

@article {KotelProp,
    AUTHOR = {Koteljanski\u{\i}, D. M.},
     TITLE = {A property of sign-symmetric matrices},
   JOURNAL = {Amer. Math. Soc. Transl. (2)},
  FJOURNAL = {American Mathematical Society Translations},
    VOLUME = {27},
      YEAR = {1963},
     PAGES = {19--23},
   MRCLASS = {15.20},
  MRNUMBER = {0151467},
       DOI = {10.1090/trans2/027/03},
       URL = {https://doi.org/10.1090/trans2/027/03},
}

@Article{KP,
  author = 	 "Witold Kra\'skiewicz and Piotr Pragacz",
  title = 	 "{Schubert polynomials and Schubert functors}",
  journal =	 "Preprint.",
  year =	 1986,
  month =	 "October"
}

@article {Kras1,
    AUTHOR = {Kra{\'s}kiewicz, Witold},
     TITLE = {Reduced decompositions in {W}eyl groups},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {16},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {293--313},
   MRCLASS = {05E15 (20C30)},
  MRNUMBER = {1330543 (96i:05181)},
MRREVIEWER = {Bernard Leclerc},
       DOI = {10.1016/0195-6698(95)90033-0},
       URL = {http://dx.doi.org/10.1016/0195-6698(95)90033-0},
}

@Article{Kras2,
  author = 	 "Witold Kra\'skiewicz",
  title = 	 "{Reduced decompositions in hyperoctahedral group}",
  journal =	 "C. R. Acad. Sci. Paris, Serie I",
  year =	 1989,
  volume =	 309,
  pages =	 "903-904"
}

@article {KrattSchlossMulti,
    AUTHOR = {Krattenthaler, Christian and Schlosser, Michael},
     TITLE = {A new multidimensional matrix inverse with applications to
              multiple {$q$}-series},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {204},
      YEAR = {1999},
    NUMBER = {1-3},
     PAGES = {249--279},
}

@Incollection{KruskalNumber,
  author = 	 "J. Kruskal",
  title = 	 "The number of simplices in a complex",
  booktitle =    "Mathematical Optimization Techniques", 
  publisher =    "University of California Press",
  address =      "Berkeley, CA",		  
  year =	 "1963",
  pages =        "251--278"
}
		  		  
@Article{kumar,
  author = 	 "Shrawan Kumar",
  title = 	 "The  nil {Hecke} ring  and singularity of {Schubert}
		  varieties",
  journal =	 "preprint",
  year =	 1996,
  month =	 "April"
}

@PhdThesis{Lam1,
  author = 	 "Tao Kai Lam",
  title = 	 "{B and D Analogues of Stable Schubert Polynomials and
		  Related Insertion Algorithms}", 
  school = 	 "MIT",
  year = 	 1995
}


@Unpublished{KurTsuChrom,
  author = 	 "Masamichi Kuroda and Shuhei Tsujie",
  title = 	 "Chromatic signed-symmetric functions of signed graphs",
  note =         "Preprint {\tt math.CO/2101.03018} on {ArXiv}",
  year =	 2021
}

@Article{Lam2,
  author = 	 "Tao Kai Lam",
  title = 	 "{$B_n$ Stanley Symmetric Functions}",
  journal =	 "Discrete Math.",
  volume =       157,		  
  year =	 1996,
  number =	 "1-3",
  pages =	 "241-270"
}

@Article{Lam3,
  author = 	 "Tao Kai  Lam",
  title = 	 "{Superfication of the Stanley Symmetric Functions}",
  journal =	 "In preparation",
  year =	 1996
}

@book{kschurbook,
    AUTHOR = {Lam, Thomas and Lapointe, Luc and Morse, Jennifer and
              Schilling, Anne and Shimozono, Mark and Zabrocki, Mike},
     TITLE = {{$k$}-{S}chur functions and affine {S}chubert calculus},
    SERIES = {Fields Institute Monographs},
    VOLUME = {33},
 PUBLISHER = {Springer, New York; Fields Institute for Research in
              Mathematical Sciences, Toronto, ON},
      YEAR = {2014},
     PAGES = {viii+219},
      ISBN = {978-1-4939-0681-9; 978-1-4939-0682-6},
   MRCLASS = {05-02 (05E05 14N15)},
  MRNUMBER = {3379711},
MRREVIEWER = {Arthur L. B. Yang},
}

@Unpublished{LamPCell,
  author = 	 "Thomas Lam and Pavlo Pylyavskyy",
  title = 	 "Cell transfer and monomial positivity",
  note =         "In preparation",
  year =	 2005
}

@article {LPPSNN,
    AUTHOR = {Lam, Thomas and Postnikov, Alexander and Pylyavskyy, Pavlo},
     TITLE = {Schur positivity and {S}chur log-concavity},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {129},
      YEAR = {2007},
    NUMBER = {6},
     PAGES = {1611--1622},
}

@article {LPTLPfaff,
    AUTHOR = {Lam, Thomas and Pylyavskyy, Pavlo},
     TITLE = {{Temperley-Lieb} pfaffinants and {Schur} {$Q$}-positivity 
conjectures},
   JOURNAL = {Adv. Math.},
    VOLUME = {218},
      YEAR = {2008},
    NUMBER = {5},
     PAGES = {1654--1684}
}

@Unpublished{LPLoop1,
  author = 	 "Thomas Lam and Pavlo Pylyavskyy",
  title = 	 "Total positivity in loop groups {I}: whirls and curls",
  note =         "Preprint {\tt math.CO/0812.0840} on {ArXiv}",
  year =	 2008
}

@Unpublished{LPLoop2,
  author = 	 "Thomas Lam and Pavlo Pylyavskyy",
  title = 	 "Total positivity in loop groups {II}: {Chevalley} generators",
  note =         "Preprint {\tt math.CO/0906.0610} on {ArXiv}",
  year =	 2009
}

@article {LambertTheta,
    AUTHOR = {Lambert, Jordan},
     TITLE = {Theta-vexillary signed permutations},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {25},
      YEAR = {2018},
    NUMBER = {4},
     PAGES = {Paper No. 4.53, 30},
   MRCLASS = {05A05},
  MRNUMBER = {3907784},
       DOI = {10.37236/8023},
       URL = {https://doi.org/10.37236/8023},
}


@Article{LakSan,
  author =       "V. Lakshmibai and B. Sandhya",
  title =        "Criterion for smoothness of {Schubert} Varieties in {$SL(n)/B$}",
  journal =      "Proc. Indian Acad. Sci. (Math Sci.)",
  year =         1990,
  volume =       100,
  number =       1,
  pages =        "45-52"
}

@Article{lak-song,
  author = 	 "V. Lakshmibai and M. Song",
  title = 	 "A Criterion for Smoothness of {Schubert} Varieties
		  in {$Sp(2n)/B$}",
  journal =	 "J. Algebra",
  year =	 1997,
  volume =	 189,
  pages =	 "332-352"
}

@Article{Laksov,
  author = 	 "Dan Laksov",
  title = 	 "{Remarks on Giovanni Zeno Giambelli's Work and Life }",
  journal =	 "Rendiconti del Circolo Matematico di Palermo",
  year =	 1994,
  series =	 2,
  number =	 36,
  pages =	 "207-218"
}

@article {LLMTableau,
    AUTHOR = {Lapointe, L. and Lascoux, A. and Morse, J.},
     TITLE = {Tableau atoms and a new {M}acdonald positivity conjecture},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {116},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {103--146},
     CODEN = {DUMJAO},
   MRCLASS = {05E05 (05E10)},
  MRNUMBER = {1950481 (2004c:05208)},
MRREVIEWER = {Michael A. Zabrocki},
       DOI = {10.1215/S0012-7094-03-11614-2},
       URL = {http://dx.doi.org/10.1215/S0012-7094-03-11614-2},
}



@Article{LLTRibbon,
    AUTHOR = {Lascoux, Alain and Leclerc, Bernard and Thibon, Jean-Yves},
     TITLE = {Ribbon tableaux, {H}all-{L}ittlewood functions, quantum affine
              algebras, and unipotent varieties},
   JOURNAL = {J. Math. Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {38},
      YEAR = {1997},
    NUMBER = {2},
     PAGES = {1041--1068}, 
       DOI = {10.1063/1.531807},
       URL = {https://doi.org/10.1063/1.531807},
}

@Article{LS1,
  author = 	 {A. Lascoux and M.-P. Sch\"utzenberger},
  title = 	 "{Polynomes de Schubert}",
  journal =	 "C.R. Acad. Sci. Paris",
  year =	 1982,
  volume =	 294,
  pages =	 "447--450"
}


@Article{LS2,
  author = 	 {A. Lascoux and M.-P. Sch\"utzenberger},
  title = 	 "{Schubert Polynomials and  the Littlewood-Richardson Rule}",
  journal =	 "Letters in Math. Physics",
  year =	 1985,
  volume =	 10,
  pages =	 "111--124"
}


@Article{LS3,
  author = 	 {A. Lascoux and M.-P. Sch\"utzenberger},
  title = 	 "{Schubert and Grothendieck Polynomials}",
  journal =	 "Preprint.",
  year =	 1988
}

@Article{LS4,
  author = 	 {A. Lascoux and M.-P. Sch\"utzenberger},
  title = 	 "{Fonctorialit\'e des  Polyn\^omes de Schubert}",
  journal =	 "Contemp. Math.",
  year =	 1989,
  volume =	 88,
  pages =	 "585--598"
}

@Article{LS5,
  author = 	 {A. Lascoux and M.-P. Sch\"utzenberger},
  title = 	 "{Tableaux and Non  Commutative Schubert Polynomials}",
  journal =	 "Funk. Anal. and Appl.",
  year =	 1989,
  volume =	 23,
  pages =	 "63--64"
}


@Article{LS6,
  author = 	 {A. Lascoux and M.-P. Sch\"utzenberger},
  title = 	 "{Structure de Hopf de l'anneau de cohomologie et de
		  l'anneau de Grothendieck d'une variete de drapeaux}",
  journal =	 "Comptes Rendus Acad. Sci. Paris Ser. I Math.",
  year =	 1982,
  volume =	 295,
  pages =	 "629--633"
}


@Article{LS7,
    AUTHOR = {Lascoux, Alain and Sch\"utzenberger, Marcel-P.},
     TITLE = {Le mono\"ide plaxique},
 BOOKTITLE = {Noncommutative structures in algebra and geometric
              combinatorics ({N}aples, 1978)},
    SERIES = {Quad. ``Ricerca Sci.''},
    VOLUME = {109},
     PAGES = {129--156},
 PUBLISHER = {CNR, Rome},
      YEAR = {1981},
   MRCLASS = {20C30 (05A99 20M10)},
  MRNUMBER = {646486},
MRREVIEWER = {Hubert\ Grassmann},
}


@Article{LS8,
  author = 	 {A. Lascoux and M.-P. Sch\"utzenberger},
  title = 	 "{Interpolation de Newton A Plusieurs Variables}",
  journal =	 "Seminare D'Algebre, Lecture Notes in Math.",
  year =	 "1983--1984",
  volume =	 1146,
  pages =	 "161--175"
}



@Article{LS9,
  author = 	 {Alain Lascoux and Marcel-Paul Sch\"utzenberger},
  title = 	 {Symmeterization operators on polynomial rings},
  journal = 	 {Funct. Anal. Appl.},
  year = 	 1987,
  volume =	 21,
  pages =	 {77--78}
}


@Article{LS10,
  author = 	 {Alain Lascoux and Marcel-Paul Sch\"utzenberger},
  title = 	 {D\'ecompositions dans l'alg\`ebre des diff\'erences divis\'ees},
  journal = 	 {Discrete Math.},
  year = 	 1992,
  volume =	 99,
  pages =	 {165--179}
}

@incollection {LS11,
    AUTHOR = {Lascoux, Alain and Sch{\"u}tzenberger, Marcel-Paul},
     TITLE = {Polyn\^omes de {K}azhdan \& {L}usztig pour les
              grassmanniennes},
 BOOKTITLE = {Young tableaux and Schur functors in algebra and geometry
              (Toru\'n, 1980)},
    SERIES = {Ast\'erisque},
    VOLUME = {87},
     PAGES = {249--266},
 PUBLISHER = {Soc. Math. France},
   ADDRESS = {Paris},
      YEAR = {1981},
   MRCLASS = {14M15 (20G05)},
  MRNUMBER = {MR646823 (83i:14045)},
MRREVIEWER = {James E. Humphreys},
}


@Article{LSTreillis,
  author = 	 "A. Lascoux and M. P. {Sch\"utzenberger}",
  title = 	 "Treillis et bases des groupes de {Coxeter}",
  journal =	 "Electron. J. Combin.",
  year =	 1996,
  volume =	 3,
  number =       2,
  note =         {Research paper 27, 35 pp.\ (electronic)}		  
}

@Article{LSYin,
  author = 	 "A. Lascoux",
  title = 	 "Potentiel {Yin} sur le groupe {sym\'etrique}",
  journal =	 "S\'em. Lothar. Combin.",
  year =	 1996,
  volume =	 38,
  note =         {Art. B38a, 12 pp.\ (electronic)}		  
}



@Article{Lascoux95,
  author = 	 "Alain Lascoux",
  title = 	 "{Polynômes de Kazhdan-Lusztig pour les variétés de Schubert vexillaires. (French) [Kazhdan-Lusztig polynomials for vexillary Schubert
varieties]}",
  journal =	 "C. R. Acad. Sci. Paris Sér. I Math.",
  volume =	 321,
  pages =	 "667--670",
  number =	 6,
  year =	 1995
}
		  
@Article{LLT,
  author = 	 {Alain Lascoux and Bernard Leclerc and Jean-Yves Thibon},
  title = 	 {Flag Varieties and the Yang-Baxter Equation},
  journal = 	 {Letters in Math. Pys.},
  year = 	 {Dec. 1995},
  volume =	 {preprint}
}

@Article{Lawler73,
  author = 	 "E. Lawler",
  title = 	 "Optimal sequencing of a single maching subject to precedence
		  constraints",
  journal = 	 "Management Sci.",
  year = 	 1973,
  volume =	 19,
  pages =        "544--546"
}
		  		  
@Manual{Leach,
  author =       "Robert Leachman",
  title =        "The Economics and Dynamics of Production",
  year =         1992,
  organization = "UC-Berkeley department of Operations Research and
                  Industrial Engineering",
  note =         "Edited by M. Skandera"
}

@article {LeclercThibonRSCrystal,
    AUTHOR = {Leclerc, Bernard and Thibon, Jean-Yves},
     TITLE = {The {R}obinson-{S}chensted correspondence, crystal bases, and
              the quantum straightening at {$q=0$}},
      NOTE = {The Foata Festschrift},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {3},
      YEAR = {1996},
    NUMBER = {2},
     NOTE = {Research Paper 11, 24 pp.},
}

@article {LeclercToffin,
    AUTHOR = {Leclerc, Bernard and Toffin, Philippe},
     TITLE = {A simple algorithm for computing the global crystal basis of
              an irreducible {$U\sb q({\rm sl}\sb n)$}-module},
   JOURNAL = {Internat. J. Algebra Comput.},
  FJOURNAL = {International Journal of Algebra and Computation},
    VOLUME = {10},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {191--208},
}

@unpublished{LewickeTNN,
  author = 	 "John Paul Lewicke",
  title = 	 "The existence and construction of some total non-negativity criteria",
  year =	 2004,
  note =         "unpublished REU paper"
}

@article {LiebPerm,
    AUTHOR = {Lieb, Elliott},
     TITLE = {Proofs of some conjectures on permanents},
   JOURNAL = {J. Math. Mech.},
    VOLUME = {16},
      YEAR = {1966},
     PAGES = {127--134},
   MRCLASS = {15.20},
  MRNUMBER = {0202745},
MRREVIEWER = {M. Marcus},
       DOI = {10.1512/iumj.1967.16.16008},
       URL = {https://doi.org/10.1512/iumj.1967.16.16008},
}

@Article{LinVrep,
  author = 	 "B. {Lindstr\"om}",
  title = 	 "On the vector representations of induced matroids",
  journal = 	 "Bull. London Math. Soc.",
  year = 	 1973,
  volume =	 5,
  pages =        "85--90"
}

@book {LittlewoodTGC,
    AUTHOR = {Littlewood, Dudley E.},
     TITLE = {The {T}heory of {G}roup {C}haracters and {M}atrix
              {R}epresentations of {G}roups},
 PUBLISHER = {Oxford University Press},
   ADDRESS = {New York},
      YEAR = {1940},
     PAGES = {viii+292},
   MRCLASS = {20.0X},
  MRNUMBER = {MR0002127 (2,3a)},
MRREVIEWER = {R. Brauer},
}

@article {LFMPMIOsc,
    AUTHOR = {Liu, Xiao Ping and Fallat, Shaun M.},
     TITLE = {Multiplicative principal-minor inequalities for a class of
              oscillatory matrices},
   JOURNAL = {JIPAM. J. Inequal. Pure Appl. Math.},
  FJOURNAL = {JIPAM. Journal of Inequalities in Pure and Applied
              Mathematics},
    VOLUME = {9},
      YEAR = {2008},
    NUMBER = {4},
     PAGES = {Article 92, 18}
}

		  
@Article{Loewner,
  author = 	 "C. Loewner",
  title = 	 "On totally positive matrices",
  journal = 	 "Math. Z.",
  year = 	 1955,
  volume =	 63,
  pages =        "338--340"
}

@article {LuceSemiorder,
    AUTHOR = {Luce, R. Duncan},
     TITLE = {Semiorders and a theory of utility discrimination},
   JOURNAL = {Econometrica},
  FJOURNAL = {Econometrica. Journal of the Econometric Society},
    VOLUME = {24},
      YEAR = {1956},
     PAGES = {178--191},
   MRCLASS = {90.0X},
  MRNUMBER = {0078632},
}

@Book{Luen,
  author = 	 "D. Luenberger",
  title = 	 "Introduction to Dynamic Systems",
  publisher = 	 "Wiley",
  year = 	 1979,
}


@book{LusztigCRGFF,
    AUTHOR = {Lusztig, George},
     TITLE = {Characters of Reductive Groups Over a Finite Field},
    SERIES = {Annals of Mathematics Studies},
    VOLUME = {107},
 PUBLISHER = {Princeton University Press},
   ADDRESS = {Princeton, NJ},
      YEAR = {1984},
}

@Incollection{LusztigCAWG,
  author = 	 "G. Lusztig",
  title = 	 "Cells in affine {W}eyl groups",
  booktitle =    "Algebraic Groups and Related Topics (Kyoto/Nagoya 1983)",
  year =	 1985,
  series =       "Adv. Stud. Pure Math",
  volume =       6,  
  publisher = 	 "North-Holland",
  address =	 "Amsterdam",
  pages =	 "255--287"
}		  

@article {LusztigCBTensor,
    AUTHOR = {Lusztig, G.},
     TITLE = {Canonical bases in tensor products},
   JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
  FJOURNAL = {Proceedings of the National Academy of Sciences of the United
              States of America},
    VOLUME = {89},
      YEAR = {1992},
    NUMBER = {17},
     PAGES = {8177--8179},
}

@article{LusztigCbaqea,
  author =       {G. Lusztig},
  title =        {Canonical bases arising from quantized enveloping algebras},
  journal =      {J. Amer. Math. Soc.},
  year =         {1990},
  volume =       {3},
  pages =        {447--498},
} 

@book {LusztigHAUP,
    AUTHOR = {Lusztig, G.},
     TITLE = {Hecke algebras with unequal parameters},
    SERIES = {CRM Monograph Series},
    VOLUME = {18},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2003},
     PAGES = {vi+136},
   MRCLASS = {20C08 (20F55)},
  MRNUMBER = {1974442 (2004k:20011)},
MRREVIEWER = {G{\"o}tz Pfeiffer},
}

@book{LusztigIntroQG,
    AUTHOR = {Lusztig, George},
     TITLE = {Introduction to Quantum Groups},
    SERIES = {Progress in Mathematics},
    VOLUME = {110},
 PUBLISHER = {Birkh\"auser Boston Inc.},
   ADDRESS = {Boston, MA},
      YEAR = {1993},
}


@Incollection{LusztigTP,
    AUTHOR = {Lusztig, G.},
     TITLE = {Total positivity in reductive groups},
 BOOKTITLE = {Lie theory and geometry},
    SERIES = {Progr. Math.},
    VOLUME = {123},
     PAGES = {531--568},
 PUBLISHER = {Birkh\"{a}user Boston, Boston, MA},
      YEAR = {1994}, 
       DOI = {10.1007/978-1-4612-0261-5\_20}, 
}

@incollection {LusztigTPCB,
    AUTHOR = {Lusztig, George},
     TITLE = {Total positivity and canonical bases},
 BOOKTITLE = {Algebraic groups and {L}ie groups},
    SERIES = {Austral. Math. Soc. Lect. Ser},
    VOLUME = {9},
     PAGES = {281--295},
 PUBLISHER = {Cambridge Univ. Press},
   ADDRESS = {Cambridge},
      YEAR = {1997},
   MRCLASS = {20G20 (14P99 20G42)},
  MRNUMBER = {MR1635687 (2000j:20089)},
MRREVIEWER = {Richard Dipper},
}

@Misc{LusztigComm08,
  author = 	 "George Lusztig",
  year =         "2008",
  note = 	 "Personal communication"
}

		  
@Article{Mac,
  author = 	 "F. S. Macaulay",
  title = 	 "Some properties of enumeration in the theory of
		  modular systems",
  journal =	 "Proc. London Math. Soc.",
  year =	 1927,
  volume =	 26,
  pages =	 "531-555"
}

@Book{M1,
  author = 	 "I.G. Macdonald",
  title = 	 "{Symmetric Fuctions and Hall Polynomials}",
  publisher = 	 "Oxford University Press",
  year = 	 1979,
  address =	 "Oxford"
}

@Book{M2,
  author = 	 "I.G. Macdonald",
  title = 	 "{Notes on Schubert Polynomials}",
  publisher = 	 "Publications du LACIM",
  year = 	 1991,
  volume =	 6,
  address =	 "Universit\'e du Qu\'ebec \`a Montr\'eal"
}


@Unpublished{M3,
  author = 	 "I.G. Macdonald",
  title = 	 "{Notes on Root Systems}",
  note = 	 "Manuscript from UCSD",
  year =	 1991,
  month =	 "Winter quarter"
}


@Article{Macdonald72,
  author = 	 {I. G. Macdonald},
  title = 	 {The Poincar\'e Series of a Coxeter Group},
  journal = 	 {Math. Ann.},
  year = 	 1972,
  volume =	 199,
  pages =	 {161--174}
}

@incollection {MacLaneCoherence,
    AUTHOR = {Mac Lane, Saunders},
     TITLE = {Coherence theorems and conformal field theory},
 BOOKTITLE = {Category theory 1991 (Montreal, PQ, 1991)},
    SERIES = {CMS Conf. Proc},
    VOLUME = {13},
     PAGES = {321--328},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1992},
   MRCLASS = {18D10 (18D05 81T40)},
  MRNUMBER = {MR1192155 (94d:18010)},
MRREVIEWER = {Yu. N. Bespalov},
}

@Article{Maclaurin,
  author = 	 {C. Maclaurin},
  title = 	 {A second letter to {Martin Foulkes}, {Esq.}, concerning
the roots of equations with the demonstrations of other rules in algebra},
  journal = 	 {Phil. Trans.},
  year = 	 1729,
  volume =	 36,
  pages =	 {59-96}
}


@Book{MacMComb,
  author = 	 "P.A. MacMahon",
  title = 	 "Combinatory Analysis",
  publisher = 	 "Cambridge Univ. Press",
  year = 	 1915,
  volume =	 "1 and 2",
  address =	 "Cambridge"
}


@book {ManinQNoncommG,
    AUTHOR = {Manin, Yu. I.},
     TITLE = {Quantum groups and noncommutative geometry},
 PUBLISHER = {Universit\'e de Montr\'eal Centre de Recherches
              Math\'ematiques},
   ADDRESS = {Montreal, QC},
      YEAR = {1988},
     PAGES = {vi+91},
   MRCLASS = {17A45 (16W30 17B37 46L87 81R50)},
  MRNUMBER = {MR1016381 (91e:17001)},
MRREVIEWER = {S. Paul Smith},
}

@Article{MarcusMincGMF,
  author = 	 {M. Marcus and H. Minc},
  title = 	 {Generalized matrix functions},
  journal = 	 {Trans. Amer. Math. Soc.},
  year = 	 1965,
  volume =	 116,
  pages =	 {316-329}
}

@book {MartinSART,
    AUTHOR = {Martin, Stuart},
     TITLE = {Schur algebras and representation theory},
    SERIES = {Cambridge Tracts in Mathematics},
    VOLUME = {112},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {1993},
     PAGES = {xvi+232},
} 


@article{MathasGeneric,
    AUTHOR = {Mathas, Andrew},
     TITLE = {Some generic representations, {$W$}-graphs, and duality},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {170},
      YEAR = {1994},
    NUMBER = {1-3},
     PAGES = {322--353},
}

@book {MathasIHA,
    AUTHOR = {Mathas, Andrew},
     TITLE = {Iwahori--{H}ecke algebras and {S}chur algebras of the symmetric
              group},
    SERIES = {University Lecture Series},
    VOLUME = {15},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {1999},
     PAGES = {xiv+188},
}


@Manual{Mattuck,
  author = 	 "Arthur Mattuck",
  title = 	 "The Torch or the Firehose: a Guide to Section Teaching",
  organization = "MIT",
  year =	 1995,
}

@article{McDPClassKL,
    AUTHOR = {McDonough, T. P. and Pallikaros, C. A.},
     TITLE = {On relations between the classical and the {K}azhdan-{L}usztig
              representations of symmetric groups and associated {H}ecke
              algebras},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {203},
      YEAR = {2005},
    NUMBER = {1-3},
     PAGES = {133--144},
}

@article {McDPSubseq,
    AUTHOR = {McDonough, T. P. and Pallikaros, C. A.},
     TITLE = {On subsequences and certain elements which determine various
              cells in {$S\sb n$}},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {319},
      YEAR = {2008},
    NUMBER = {3},
     PAGES = {1249--1263},
}


@article{McWarCounter01,
    AUTHOR = {McLarnan, Timothy J. and Warrington, Gregory S.},
     TITLE = {Counterexamples to the 0-1 conjecture},
   JOURNAL = {Represent. Theory},
  FJOURNAL = {Representation Theory. An Electronic Journal of the American
              Mathematical Society},
    VOLUME = {7},
      YEAR = {2003},
     PAGES = {181--195 (electronic)},
}


@incollection {McSmythSalem,
    AUTHOR = {McKee, James and Smyth, Chris},
     TITLE = {Salem numbers of trace {$-2$} and traces of totally positive
              algebraic integers},
 BOOKTITLE = {Algorithmic number theory},
    SERIES = {Lecture Notes in Comput. Sci},
    VOLUME = {3076},
     PAGES = {327--337},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2004},
}

@article {McNNecCond,
    AUTHOR = {McNamara, Peter R. W.},
     TITLE = {Necessary conditions for {S}chur-positivity},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {28},
      YEAR = {2008},
    NUMBER = {4},
     PAGES = {495--507},
 }
		
@unpublished{vWClass,
    author = {McNamara, Peter and van Willigenburg, Stephanie},
    title =  "A combinatorial classification of skew {Schur} functions",
    year =   2006,
    note =   "Preprint available at {\tt http://www.math.ubc.ca/\%7Esteph/pub.html}"}

@article {MeadDIIW,
    AUTHOR = {Mead, D. G.},
     TITLE = {Determinantal ideals, identities, and the {W}ronskian},
   JOURNAL = {Pacific J. Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {42},
      YEAR = {1972},
     PAGES = {165--175},
}

@phdthesis{MelnikovThesis,
 author =     "A. Melnikov",
 title =      "{G}eometric {I}nterpretation of
{R}obinson-{S}chensted procedure and related orders on
{Y}oung tableaux",
 school =     "Weizmann Institute",
 year =       1992
}

@article {MelnikovOVC1,
    AUTHOR = {Melnikov, Anna},
     TITLE = {On orbital variety closures in {$\mathfrak{sl}\sb n$}. {I}.
              {I}nduced {D}uflo order},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {271},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {179--233},
}

@article {MelnikovOVC2,
    AUTHOR = {Melnikov, Anna},
     TITLE = {On orbital variety closures in {$\mathfrak{sl}\sb n$}. {II}.
              {D}escendants of a {R}ichardson orbital variety},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {271},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {698--724},
}
		
@article {MelnikovOVC3,
    AUTHOR = {Melnikov, Anna},
     TITLE = {On orbital variety closures in {$\mathfrak{sl}\sb n$}. {III}.
              {G}eometric properties},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {305},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {68--97},
}

@article {MerVanDST,
    AUTHOR = {Merris, Russell},
     TITLE = {On vanishing decomposable symmetrized tensors},
   JOURNAL = {Linear and Multilinear Algebra},
  FJOURNAL = {Linear and Multilinear Algebra},
    VOLUME = {5},
      YEAR = {1977/78},
    NUMBER = {2},
     PAGES = {79--86}
}

@article {MerWatIneq,
    AUTHOR = {Merris, Russell and Watkins, William},
     TITLE = {Inequalities and identities for generalized matrix functions},
   JOURNAL = {Linear Algebra Appl.},
  FJOURNAL = {Linear Algebra and its Applications},
    VOLUME = {64},
      YEAR = {1985},
     PAGES = {223--242}
}
		 		  

@article {MesrefAstro,
    AUTHOR = {Mesref, L.},
     TITLE = {Quantum gauge theory on the quantum anti-de {S}itter space},
   JOURNAL = {Phys. Rev. D (3)},
  FJOURNAL = {Physical Review. D. Third Series},
    VOLUME = {68},
      YEAR = {2003},
    NUMBER = {6},
     PAGES = {065007, 6},
     CODEN = {PRVDAQ},
   MRCLASS = {81T20 (83C47)},
  MRNUMBER = {MR2036590 (2004k:81234)},
}


@Article{MONK,
  author = 	 "D. Monk",
  title = 	 "{The geometry of flag manifolds}",
  journal =	 "Proc. London Math. Soc.",
  year =	 1959,
  volume =	 3,
  number =	 9,
  pages =	 "253-286"
}

@Unpublished{MSkanWLLT,
    AUTHOR = {Alejandro Morales and Mark Skandera and Jiayuan Wang},
     TITLE = {Characters and {LLT} polynomials},
    note = "In preparation",
    year = 2023
}


@Article{Muirhead,
  author = 	 "R. F. Muirhead",
  title = 	 "{Some methods applicable to identities of symmetric algebraic functions of $n$ letters}",
  journal =	 "Proc. Edinburgh Math. Soc.",
  year =	 "1902/03",
  volume =	 21,
  pages =	 "144-157"
}


@Book{MunkresAT,
  author = 	 "J. Munkres",
  title = 	 "{Elements of Algebraic Topology}",
  publisher = 	 "Addison-Wesley",
  year = 	 1984
}		  

@Article{Neg,
  author = 	 "J. Neggers",
  title = 	 "Representations of finite partially ordered sets",
  journal =	 "J. Combin. Inform. System Sci.",
  year =	 1978,
  volume =	 3,
  pages =	 "113-133"
}

@Book{Newton,
  author = 	 "I. Newton",
  title = 	 "{Arithmetica universalis: sive de compositione et resolutione arithmetica liber}",
  note =         "Opera, I.",
  year =         1732,
  publisher =    "Leiden"
}		  

@Article{OkounkovLog,
  author = 	 "A. Okounkov",
  title = 	 "Log-concavity of multiplicities with applications to characters of {$U(\infty)$}",
  journal =	 "Adv. Math.",
  year =	 1997,
  volume =	 127,
  number =	 2,
  pages =	 "258--282"
}

@misc{OEIS,
    Author = {{OEIS Foundation Inc.}},
    Note =  {Published electronically at {\tt http://oeis.org}},
    Title = {The {O}n-{L}ine {E}ncyclopedia of {I}nteger {S}equences},
} 
		 		
@Book{Oxley,
  author = 	 "J. Oxley",
  title = 	 "{Matroid Theory}",
  publisher = 	 "Oxford University Press",
  year = 	 1992
}		  


@Book{PapaSteig,
  author = 	 "C. Papadimitriou and K. Steiglitz",
  title = 	 "{Combinatorial Optimization Algorithms and Complexity}",
  publisher = 	 "Springer",
  year = 	 1998
}		  


@Misc{KPetersonComm,
  author = 	 "K. Peterson",
  year =         "2005",
  note = 	 "Personal communication"		  
}
		        	
@incollection {PfeifferCharB,
    AUTHOR = {Pfeiffer, G\"{o}tz},
     TITLE = {Character values of {I}wahori-{H}ecke algebras of type {$B$}},
 BOOKTITLE = {Finite reductive groups ({L}uminy, 1994)},
    SERIES = {Progr. Math.},
    VOLUME = {141},
     PAGES = {333--360},
 PUBLISHER = {Birkh\"{a}user Boston, Boston, MA},
      YEAR = {1997},
   MRCLASS = {20C15 (20F55)},
  MRNUMBER = {1429879},
MRREVIEWER = {Robert B\'{e}dard},
}

@Article{PopoviciuSur,
  author = 	 "T. Popoviciu",
  title = 	 "Sur un {th\'eor\`eme} de {Laguerre}",
  journal =	 "Bull. Soc. Sci. Cluj",
  volume =       "8",
  pages =        "1--4",
  year =	 1934
}

@Article{PostPieri,
  author = 	 "Alexander Postnikov",
  title = 	 "On a quantum version of {Pieri's} formula",
  journal =	 "preprint",
  year =	 1997
}


@Article{PostQuantumBruhat,
   AUTHOR = {Postnikov, Alexander},
     TITLE = {Quantum {B}ruhat graph and {S}chubert polynomials},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {133},
      YEAR = {2005},
    NUMBER = {3},
     PAGES = {699--709 (electronic)},
}


@Misc{PostComm,
  author = 	 "Alex Postnikov",
  year =         "2000",
  note = 	 "Personal communication"
}

@Article{PouzetRosen,
  author = 	 "M. Pouzet and I. G. Rosenberg",
  title = 	 "Sperner properties for groups and relations",
  journal =	 "Europ. J. Combin.",
  volume =       7,
  pages =	 "349--370",
  year =	 1986
}

@InBook{P,
  author = 	 "P. Pragacz",
  title = 	 "{Algebro-Geometric applications of Schur $S$- and
		  $Q$-polynomials}", 
  chapter = 	 6,
  booktitle =	 "Topics in Invariant Theory",
  publisher =	 "Springer Lecture Notes in Mathematics",
  year =	 1991,
  pages =	 "130--191",
  volume =	 1478
}


@Article{PR1,
  author = 	 "Piotr Pragacz and Jan Ratajski",
  title = 	 "{Formulas for Lagrangian and Orthogonal Degeneracy
		  Loci; the $\widetilde{Q}$ Approach}",
  journal =	 "preprint",
  year =	 1995
}

@Article{PR2,
  author = 	 "Piotr Pragacz and Jan Ratajski",
  title = 	 "{Pieri Type Formulas for Isotropic Grassmannians; the
		  Operator Approach}",
  journal =	 "Manuscripta Mathematica",
  year =	 1993,
  volume =	 79,
  pages =	 "127-151"
}

@Article{PR3,
  author = 	 "Piotr Pragacz and Jan Ratajski",
  title = 	 "{A Pieri-type theorem for Lagrangian and odd orthogonal Grassmannians}",
  journal =	 "Preprint MPI/94-15.; to appear in J. reine angew. Math.",
  year =	 1994,
}


@Article{PR4,
  author = 	 {Piotr Pragacz and Jan Ratajski},
  title = 	 {Formulas for Lagrangian and orthogonal
  degeneracy loci: the $\tilde{Q}$-polynomials approach},
  journal = 	 { Compositio
Math.},
  year = 	 {To appear}
}

@Article{PSPerverseNHV,
  author = 	 {Martha Precup and Eric Sommers},
  title = 	 {Perverse sheaves, nilpotent {Hessenberg} varieties, and
the modular law},
  journal = 	 {Pure Appl. Math. Q.},
  year = 	 {To appear}
}


@Article{ProctorBruhat,
  author = 	 {Robert A. Proctor},
  title = 	 {Classical {Bruhat} Orders and Lexicographic Shellability},
  journal = 	 {J. Algebra},
  year = 	 1982,
  volume =	 77,
  pages =	 {104--126},
}

@Article{PvWOnTensor,
  author = 	 {Kevin Purbhoo and Stephanie van Willigenburg},
  title = 	 {On tensor products of polynomial representations},
  journal = 	 {Canad. Math. Bull.},
  year = 	 2008,
  volume =	 51,
  number =       4,
  pages =	 {584--592}
}


@Unpublished{PylAWeb,
  author = 	 "Pavlo Pylyavskyy",
  title = 	 "{$A_2$} web immanants",
  note =         "Preprint {\tt math.CO/0712.2597} on {ArXiv}",
  year =	 2008
}

@Article{RabDim,
  author = 	 "I. Rabinovitch",
  title = 	 "The dimension of semiorders",
  journal =	 "J. Combin. Theory Ser. A",
  year =	 1978,
  volume =	 25,
  pages =	 "50--61"
}

@article{RamFrob,
    AUTHOR = {Ram, Arun},
     TITLE = {A {F}robenius formula for the characters of the {H}ecke
              algebras},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {106},
      YEAR = {1991},
    NUMBER = {3},
     PAGES = {461--488},
}

@article {RamRemAppFrob,
    AUTHOR = {Ram, Arun and Remmel, Jeffrey B.},
     TITLE = {Applications of the {F}robenius formulas for the characters of
              the symmetric group and the {H}ecke algebras of type {$A$}},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {6},
      YEAR = {1997},
    NUMBER = {1},
     PAGES = {59--87},
}

@Article{Rawrmaj,
  author = 	 "D. Rawlings",
  title = 	 "The $r$-major index",
  journal =	 "J. Combin. Theory Ser. A",
  year =	 1981,
  volume =	 31,
  pages =	 "175--183"
}

@Article{RaychevChem,
  author = 	 "P. Raychev",
  title = 	 "Quantum groups: {A}pplication to nuclear and molecular spectroscopy",
  journal =	 "Advances Quantum Chem.",
  year =	 1995,
  volume =	 26,
  pages =	 "239--357"
}

@article{ReadingOD,
    AUTHOR = {Reading, Nathan},
     TITLE = {Order dimension, strong {B}ruhat order and lattice properties
              for posets},
   JOURNAL = {Order},
  FJOURNAL = {Order. A Journal on the Theory of Ordered Sets and its
              Applications},
    VOLUME = {19},
      YEAR = {2002},
    NUMBER = {1},
     PAGES = {73--100},
}

@unpublished{Reed,
  author = 	 "B. Reed",
  title = 	 "Factorization of antiadjacency matrices of 
		  $(\mathbf{3}+\mathbf{1})$-free posets",
  month =        "Fall",
  year =	 2001,
  note =         "U. Michigan REU project"
}

@Article{ReinerParset,
  author = 	 "V. Reiner",
  title =        "Signed posets",
  journal =	 "J.\ Combin.\ Theory Ser.\ A",
  year =	 1993,
  volume =	 62,
  number =       2,
  pages =	 "324--360"
} 
		
@Article{RS,
  author = 	 "V. Reiner and M. Shimozono",
  title = 	 "{Key Polynomials and a Flagged Littlewood-Richardson Rule}"
}

@Article{RS2,
  author = 	 "V. Reiner and M. Shimozono",
  title = 	 "Plactification",
  journal =	 "J. Algebraic Combin.",
  year =	 1995,
  volume =	 4,
  pages =	 "331-351"
}

@Misc{RSWComm,
  author = 	 "V. Reiner and D. Stanton and D. White",
  year =         "2007",
  note = 	 "Personal communication"
}

@article {RSWCyclic,
    AUTHOR = {Reiner, V. and Stanton, D. and White, D.},
     TITLE = {The cyclic sieving phenomenon},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {108},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {17--50}
}

@unpublished{ReinerWelker,
  author = 	 "V. Reiner and V. Welker",
  title = 	 "On the {Charney-Davis} and {Neggers-Stanley} conjectures",
  year =	 2003,
  note =         "Preprint available at http://www.math.umn.edu/$\sim$reiner/Papers/papers.html",
}
		  
@Article{Reisner,
  author = 	 "G. Reisner",
  title = 	 "{Cohen-Macaulay} quotients of polynomial rings",
  journal =	 "Adv. Math.",
  year =	 1976,
  volume =	 21,
  pages =	 "30-49"
}

@Article{RemTrans,
  author = 	 "D. Beck and J. Remmel and T. Whitehead",
  title = 	 "The combinatorics of transition matrices between the bases of the symmetric functions and the {$B_n$} analogues",
  journal =	 "Discrete Math.",
  year =	 1996,
  volume =	 153,
  pages =	 "3--27"
}

@unpublished{RhoadesCluster,
  author = 	 "B. Rhoades",
  title = 	 "The cluster and dual canonical bases of {$\mathbb Z[x_{1,1}, \dotsc, x_{3,3}]$} are equal", 
  year =	 2009,
  note =         "Submitted"
}

@article {RhoadesCSP,
    AUTHOR = {Rhoades, Brendon},
     TITLE = {Cyclic sieving, promotion, and representation theory},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {117},
      YEAR = {2010},
    NUMBER = {1},
     PAGES = {38--76},
     CODEN = {JCBTA7},
   MRCLASS = {05E10},
  MRNUMBER = {2557880 (2011c:05369)},
MRREVIEWER = {Anna Stokke},
       DOI = {10.1016/j.jcta.2009.03.017},
       URL = {http://dx.doi.org/10.1016/j.jcta.2009.03.017},
}


@article {RSkanBitabDCB,
    AUTHOR = {Rhoades, Brendon and Skandera, Mark},
     TITLE = {Bitableaux and zero sets of dual canonical basis elements},
   JOURNAL = {Ann. Comb.},
  FJOURNAL = {Annals of Combinatorics},
    VOLUME = {15},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {499--528},
   MRCLASS = {05E10},
  MRNUMBER = {2836454},
MRREVIEWER = {Gregory S. Warrington},
       DOI = {10.1007/s00026-011-0103-8},
       URL = {http://dx.doi.org/10.1007/s00026-011-0103-8},
}
		  
@article{RSkanKLImm,
  author = 	 "B. Rhoades and M. Skandera",
  title = 	 "{Kazhdan-Lusztig} immanants and products of matrix minors", 
  journal =      "J. Algebra",
  year =	 2006,
  volume =       304,
  number =       2,
  pages =        "793-811"
}

@article {RSkanKLImm2,
    AUTHOR = {Rhoades, Brendon and Skandera, Mark},
     TITLE = {Kazhdan-{L}usztig immanants and products of matrix minors.
              {II}},
   JOURNAL = {Linear Multilinear Algebra},
  FJOURNAL = {Linear and Multilinear Algebra},
    VOLUME = {58},
      YEAR = {2010},
    NUMBER = {1-2},
     PAGES = {137--150},
   MRCLASS = {05E05 (05E10 15A15)},
  MRNUMBER = {2641529 (2011d:05386)},
MRREVIEWER = {Gregory S. Warrington},
       DOI = {10.1080/03081080701646638},
       URL = {http://dx.doi.org/10.1080/03081080701646638},
}


@article {RSkanTLImm,
    AUTHOR = {Rhoades, Brendon and Skandera, Mark},
     TITLE = {Temperley-{L}ieb immanants},
   JOURNAL = {Ann. Comb.},
  FJOURNAL = {Annals of Combinatorics},
    VOLUME = {9},
      YEAR = {2005},
    NUMBER = {4},
     PAGES = {451--494},
   MRCLASS = {20C08 (05E15 15A15)},
  MRNUMBER = {MR2205034}
}


@Book{RibProbs,
  author = 	 "K. {R\'\i bnikov}",
  title = 	 "{An\'alisis Combinatorio Problemas y Ejercicios}",
  publisher = 	 "Editorial Mir Mosc\'u",
  year = 	 1989,
  note =         "Traducido del ruso por {K. Medkov}",        
  address =	 "Moscow"
}

@article {KonniInfCone,
    AUTHOR = {Rietsch, Konstanze},
     TITLE = {The infinitesimal cone of a totally positive semigroup},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {125},
      YEAR = {1997},
    NUMBER = {9},
     PAGES = {2565--2570},
     CODEN = {PAMYAR},
   MRCLASS = {20G20 (15A48)},
  MRNUMBER = {MR1401752 (97m:20056)},
MRREVIEWER = {Donald R. King},
}

@article{KonniIBruhat,
    AUTHOR = {Rietsch, Konstanze},
     TITLE = {Intersections of {B}ruhat cells in real flag varieties},
      NOTE = {With an appendix by G. Lusztig},
   JOURNAL = {Internat. Math. Res. Notices},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {1997},
    NUMBER = {13},
     PAGES = {623--640},
   MRCLASS = {14M15 (20G20)},
  MRNUMBER = {MR1459628 (98f:14038)},
MRREVIEWER = {Eric N. Sommers},
}

@article {KonniQCohGrass,
    AUTHOR = {Rietsch, Konstanze},
     TITLE = {Quantum cohomology rings of {G}rassmannians and total
              positivity},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {110},
      YEAR = {2001},
    NUMBER = {3},
     PAGES = {523--553},
     CODEN = {DUMJAO},
   MRCLASS = {14N35 (14M15 20G20)},
  MRNUMBER = {MR1869115 (2003c:14063)},
MRREVIEWER = {Andrew Kresch},
}

@incollection{KonniTPWomen,
    AUTHOR = {Rietsch, Konstanze},
     TITLE = {Total positivity, flag varieties and quantum cohomology},
 BOOKTITLE = {European women in mathematics (Malta, 2001)},
     PAGES = {149--167},
 PUBLISHER = {World Sci. Publ., River Edge, NJ},
      YEAR = {2003},
   MRCLASS = {14N35 (14M15)},
  MRNUMBER = {MR2012203 (2004k:14097)},
MRREVIEWER = {I. Dolgachev},
}

@article {KonniTPT,
    AUTHOR = {Rietsch, Konstanze},
     TITLE = {Totally positive {T}oeplitz matrices and quantum cohomology of
              partial flag varieties},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {16},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {363--392 (electronic)},
   MRCLASS = {14N35 (14N15 15A48)},
  MRNUMBER = {MR1949164 (2004d:14081)},
MRREVIEWER = {Frank Sottile},
}

@Unpublished{RSEschers,
  author = 	 "Alexandre Rok and Andras Szenes",
  title = 	 "{Eschers} and {Stanley's} chromatic $e$-positiviey conjecture",
  note =	 "Preprint {\tt math.CO/2305.00963} on {ArXiv}",
  year =	 2023
}


@Book{RoubenVinc,
  author = 	 "M. Roubens and P. Vincke",
  title = 	 "Preference Modelling",
  year =	 1985,
  publisher = 	 "Springer-Verlag",
  series =       "Lecture Notes in Economics and Mathematical Systems",	 
  volume =       250,
  address =	 "Berlin"
}

@article {RyanSchubert,
    AUTHOR = {Ryan, Kevin M.},
     TITLE = {On {S}chubert varieties in the flag manifold of {${\rm
              Sl}(n,{\bf C})$}},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {276},
      YEAR = {1987},
    NUMBER = {2},
     PAGES = {205--224},
     CODEN = {MAANA},
   MRCLASS = {14M15 (14M17)},
  MRNUMBER = {MR870962 (88e:14061)},
MRREVIEWER = {Konrad Drechsler},
}


@article {RyffOnMuirhead,
    AUTHOR = {Ryff, John V.},
     TITLE = {On {M}uirhead's theorem},
   JOURNAL = {Pacific J. Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {21},
      YEAR = {1967},
     PAGES = {567--576},
}

@Article{SachsHex,
  author = 	 "H. Sachs",
  title = 	 "Perfect matchings in hexagonal systems",
  journal =	 "Combinatorica",
  year =	 1984,
  volume =	 4,
  number =	 1,
  pages =	 "89--99"
}

		  		  
@Book{Sag,
  author = 	 "B. Sagan",
  title = 	 "The Symmetric Group",
  publisher = 	 "Springer",
  year = 	 2001,
  address =	 "New York"		  
}

@Article{Sag2,
  author = 	 "B. E. Sagan",
  title = 	 "{Shifted tableaux, Schur $Q$-functions, and a
		  conjecture of R.~Stanley}",
  journal =	 "J. Combin. Theory Ser. A",
  year =	 1987,
  volume =	 45,
  number =	 1,
  pages =	 "62--103"
}
		  
@Article{SagGebChrom,
  author = 	 "B. E. Sagan and D. Gebhard",
  title = 	 "A chromatic symmetric function in noncommuting variables",
  journal =	 "J. Algebraic Combin.",
  year =	 2001,
  volume =	 13,
  pages =	 "227-255"
}

@Book{Sam,
  author = 	 "Marilyn Schauer Samuels",
  title = 	 "The Technical Writing Process",
  publisher = 	 "Oxford University Press",
  year = 	 1989
}

@Article{Sands,
  author = 	 "B. Sands",
  title = 	 "Reconstruction of partially ordered sets",
  journal =	 "Order",
  year =	 1985,
  volume =	 1,
  pages =	 "311--313"
}		  

@article {SasamotoHalf,
    AUTHOR = {Sasamoto, T. and Imamura, T.},
     TITLE = {Fluctuations of the one-dimensional polynuclear growth model
              in half-space},
   JOURNAL = {J. Statist. Phys.},
  FJOURNAL = {Journal of Statistical Physics},
    VOLUME = {115},
      YEAR = {2004},
    NUMBER = {3-4},
     PAGES = {749--803},
     CODEN = {JSTPSB},
   MRCLASS = {82C44 (82C43)},
  MRNUMBER = {MR2054161 (2005d:82112)},
MRREVIEWER = {Estelle L. Basor},
}
		  
@Article{Schensted,
  author = 	 "C. Schensted",
  title = 	 "{Longest Increasing and Decreasing Subsequences}",
  journal =	 "Canad. J. Math.",
  year =	 1961,
  volume =	 13,
  pages =	 "179--191"
}

@Article{Schlomilch,
  author = 	 "O. {Schl\"omilch}",
  title = 	 "{\"Uber Mittel gr\"ossen verschiedener Ordnung}",
  journal =	 "Z. Math. Phys.",
  year =	 1858,
  volume =	 3,
  pages =	 "301--308"
}

@PhdThesis{SchurThesis,
    AUTHOR = {Schur, I.},
     TITLE = {\"{U}ber eine {K}lasse von {M}atrizen die sich einer gegebenen
     Matrix zuordnen lassen},
      YEAR = {1901},
    SCHOOL = {University of Berlin},
}

@article {SchurUberendliche,
    AUTHOR = {Schur, I.},
     TITLE = {\"{U}ber endliche {G}ruppen und {H}ermitesche {F}ormen},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {1},
      YEAR = {1918},
    NUMBER = {2-3},
     PAGES = {184--207},
}

@Article{SchurVerteilung,
  author = 	 "I. Schur",
  title = 	 "{\"Uber die Verteilung der Wurzeln bei gewissen 
                   algebraischen Gleichungen mit ganzzahligen 
                   Koeffizienten}",
  journal =	 "Math. Z.",
  year =	 1918,
  volume =	 1,
  pages =	 "377-402"
}


@Incollection{SchutChar,
  author = 	 "M. P. {Sch\"utzenberger}",
  title = 	 "A characteristic property of certain polynomials of
		  {E. F. Moore} and {C. E. Shannon}",
  number =       55,
  year =	 1959,
  booktitle =    "RLE Quarterly Progress Report",
  publisher =    "MIT Research Laboratory of Electronics",
  pages =	 "117-118"
}		  		  

@article {SchwingerTQF5,
    AUTHOR = {Schwinger, Julian},
     TITLE = {The theory of quantized fields. {V}},
   JOURNAL = {Physical Rev. (2)},
    VOLUME = {93},
      YEAR = {1954},
     PAGES = {615--628},
}
		
		  
@Article{ScottSup,
  author = 	 "D. Scott and P. Suppes",
  title = 	 "Foundational aspects of theories of measurement",
  journal =	 "J. Symbol. Logic",
  year =	 1958,
  volume =	 23,
  pages =	 "233--247"
}


@book {Shafarevich,
    AUTHOR = {Shafarevich, I. R.},
     TITLE = {Basic algebraic geometry},
   EDITION = {Study},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1977},
     PAGES = {xv+439},
   MRCLASS = {14-01},
  MRNUMBER = {MR0447223 (56 \#5538)},
}

@InBook{Shannon,
  author = 	 "Claude E. Shannon",
  title = 	 "{Scientific Aspects of Juggling}",
  booktitle =	 "Claude Elwood Shannon Collected Papers",
  publisher =	 "IEEE Press",
  year =	 1992,
  pages =	 "850--864",
}		  

@Misc{ShareshianComm18,
  author = 	 "John Shareshian",
  year =         "2018",
  note = 	 "Personal communication"
}


@Article{SWachsqEulerian,
  author = 	 "J. Shareshian and M. L. Wachs",
  title = 	 "{$q$-Eulerian} polynomials: excedance number and major index",
  journal =	 "Electron. Res. Announc. Amer. Math. Soc.",
  year =	 2007,
  volume =	 13,
  pages =	 "33--45"
}

@Inproceedings{SWachsChromQ,
  author = 	 "John Shareshian and Michelle Wachs",
  title = 	 "Chromatic quasisymmetric functions and {Hessenberg} varieties",
  booktitle =    "Configuration Spaces", 
  editor =       "A Bjorner and F Cohen and C De~Concini and C Procesi and M Salvetti",
  year =	 2012,
  publisher =    "Edizione Della Normale",
  address =      "Pisa",
  pages =	 "433--460"
}

@article {SWachsChromQF,
    AUTHOR = {Shareshian, John and Wachs, Michelle L.},
     TITLE = {Chromatic quasisymmetric functions},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {295},
      YEAR = {2016},
     PAGES = {497--551},
   MRCLASS = {05E05 (14M15)},
  MRNUMBER = {3488041},
MRREVIEWER = {Meesue Yoo},
       DOI = {10.1016/j.aim.2015.12.018},
       URL = {https://doi.org/10.1016/j.aim.2015.12.018},
}

@Article{SiegelTr,
  author = 	 "C. L. Siegel",
  title = 	 "The trace of totally positive and real 
                  algebraic integers",
  journal =	 "Ann. of Math.",
  year =	 1945,
  volume =	 46,
  number =       2,
  pages =	 "302--312"
}

@Article{Sim,
  author = 	 "R. Simion",
  title = 	 "A multiindexed {Sturm} sequence of polynomials and
                   unimodality of certain combinatorial sequences",
  journal =	 "J. Combin. Theory Ser. A",
  year =	 1984,
  volume =	 36,
  pages =	 "15-22"
}

@Article{SS,
  author = 	 "R. Simion and F.W. Schmidt",
  title = 	 "Restricted permutations",
  journal =	 "Europ. J. Combin.",
  year =	 1985,
  volume =	 6,
  pages =	 "383--406"
}

@Book{Sipser,
  author = 	 "M. Sipser",
  title = 	 "{Introduction to the Theory of Computation}",
  publisher = 	 "PWS Publishing Company",
  note =         "Preliminary edition",
  year = 	 1996
}		  

@PhdThesis{SkanThesis,
  author = 	 "M. Skandera",
  title = 	 "Chain Polynomials and Permutation Statistics",
  school = 	 "MIT",
  year = 	 2000,
  address =	 "Cambridge, MA"
}

@Article{Skan3+1,
  author = 	 "M. Skandera",
  title = 	 "A characterization of $(\mathbf{3+1})$-free posets",
  journal =	 "J. Combin. Theory Ser. A",
  year =	 2001,
  volume = 	 93,
  number =       2,
  pages =        {231--241}		  
}

@Unpublished{SkanCCSArx2,
    AUTHOR = {Skandera, Mark},
     TITLE = {Characters and chromatic symmetric functions},
    note =       "Preprint {\tt math.CO/2010.00458v2} on {ArXiv}",
    year =	 2020
}

@article{SkanCCS,
    AUTHOR = {Skandera, Mark},
     TITLE = {Characters and chromatic symmetric functions},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {28},
      YEAR = {2021},
    NUMBER = {2},
     NOTE = {Research Paper P2.19, 39 pages},
}


@unpublished{SkanDoubleKLO,
  author = 	 "M. Skandera",
  title = 	 "Double parabolic {Kazhdan-Lusztig} polynomials and an immanant formulation of the dual canonical basis (overkill version)",
  note =	 "In preparation",
  year =	 2009
}

@unpublished{LSkanDoubleKL,
  author = 	 "J. Lambright and M. Skandera",
  title = 	 "Double parabolic {Kazhdan-Lusztig} polynomials and an immanant formulation of the dual canonical basis",
  note =	 "In preparation",
  year =	 2010
}

@incollection{LSkanCFDPR,
  author = 	 "J. Lambright and M. Skandera",
  title = 	 "Combinatorial Formulas for Double Parabolic {$R$-polynomials}",
BOOKTITLE = {Proceedings of the 22nd Interntational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2010)},
    SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AO},
     PAGES = {857--868},
 PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
      YEAR = {2010},
 }

@Article{SkanCBasis3,
  author = 	 "M. Skandera",
  title = 	 "The cluster basis of $\mathbb{Z}[x_{1,1},\dotsc,x_{3,3}]$",
  year =	 2007,
  journal =      "Electron. J. Combin.",
  volume =       14,
  number =       1,
  note =         "Research paper 76, 22 pp."	   
}

@Article{SkanDmc,
  author = 	 "M. Skandera",
  title = 	 "Dumont's statistic on words",
  year =	 2001,
  journal =      "Electron. J. Combin.",
  volume =       8,
  number =       1,
  note =         "Research paper 11, 19 pp."	   
}
 
@Article{SkanPart,
  author = 	 "M. Skandera",
  title = 	 "An {Eulerian} partner for inversions",
  journal =	 "S\'em. Lothar. Combin.",
  volume =	 46,
  note =         {Art.\ B46d, 19 pp.},		  
  year =	 2001
}

@Unpublished{SkanHyperGC,
  author = 	 {Skandera, Mark},
  title = 	 {Hyperoctahedral group characters and a type-{BC} analog of graph coloring},
  year =	 {2024},
  NOTE = {Preprint {\tt math.CO/2402.04148} on {ArXiv}},
}


@Manual{SkanBTS,
  author = 	 "M. Skandera",
  title = 	 "{Gu\'\i a} Para los Interfases BTS-Reuters",
  year =	 1995,
  organization = "Banco Santander",
  address      = "Madrid"
}

@Article{SkanGenFnWreath,
    AUTHOR = {Skandera, Mark},
     TITLE = {Generating functions for monomial characters of wreath products
     $\mathbb{Z}/d\mathbb{Z} \wr \mathfrak{S}_n$},
   JOURNAL = {Enum. Combin. Appl.},
  FJOURNAL = {Enumerative Combinatorics and Applications},     
    VOLUME = {1},
      YEAR = {2021},
    NUMBER = {2},
     NOTE = {Paper S2R10, 10 pages},
}


@Article{Skanhsurvey,
  author = 	 "M. Skandera",
  title = 	 "Interpretaciones del $h$-vector",
  journal =	 "Bol. Asoc. Mat. Venez.",
  volume = 	 2,
  pages =        "141--174",
  year =	 2001
}
		  

@Article{SkanIneq,
  author = 	 "M. Skandera",
  title = 	 "Inequalities in products of minors of totally
		  nonnegative matrices",
  year =	 "2004",
  volume =       20,
  number =       2,
  journal =      "J. Algebraic Combin.",	   
  pages =        "195--211",
       DOI = {10.1023/B:JACO.0000047282.21753.ae},
       URL = {https://doi.org/10.1023/B:JACO.0000047282.21753.ae},
}

@manual{SkanIntro,
  author = 	 "M. Skandera",
  title = 	 "{Introduction to Combinatorics and Graph Theory}",
  year =	 2002,
  note =         "Unpublished lecture notes for {U. Michigan} course
		  {Math} 565"	   
}

@manual{SkanIntroTNN,
  author = 	 "M. Skandera",
  title = 	 "{Introduction to Total Nonnegativity}",
  year =	 2002,
  note =         "Handout for undergraduate presentation"	   
}


@Article{SkanNNDCB,
  author = 	 "M. Skandera",
  title = 	 "On the dual canonical and {Kazhdan}-{Lusztig} bases and 3412, 4231-avoiding permutations",
  year =	 2008,
  volume =       212,
  journal =      "J.\ Pure Appl.\ Algebra"
}


@unpublished{SkanPTImmRep,
  author = 	 "M. Skandera",
  title = 	 "Path tableaux and immanants related to representations of {$S_n$}",
  note =	 "In preparation",
  year =	 2004
}

@unpublished{SkanPerm,
  author = 	 "M. Skandera",
  title = 	 "Interpretations of the permanent of a totally nonnegative matrix",
  note =	 "In preparation",
  year =	 2020
}

@Unpublished{SkanBGenFn,
    AUTHOR = {Skandera, Mark},
     TITLE = {Symmetric generating functions for
     hyperoctahedral group characters},
    note =       "In preparation",
    year =	 2021
}


@article{SkanReed,
  author = 	 "M. Skandera and B. Reed",
  title = 	 "Total Nonnegativity and $(\mathbf{3}+\mathbf{1})$-free posets",
  year =	 2003,
  journal =      "J. Combin. Theory Ser. A",
  volume =       103,
  pages =        "237--256"
}		  

@unpublished{SkanTnnp,
  author = 	 "M. Skandera",
  title = 	 "On totally nonnegative polynomials",
  year =	 2003,
  note =         "In preparation"	   
}

@incollection {CSSkanPathTab,
    AUTHOR = {Clearman, Sam and Shelton, Brittany and Skandera, Mark},
     TITLE = {Path tableaux and combinatorial interpretations of immanants
              for class functions on {$S_n$}},
 BOOKTITLE = {23rd {I}nternational {C}onference on {F}ormal {P}ower {S}eries
              and {A}lgebraic {C}ombinatorics ({FPSAC} 2011)},
    SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AO},
     PAGES = {233--244},
 PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
      YEAR = {2011},
   MRCLASS = {05E05 (05A17 05E10)},
  MRNUMBER = {2820713},
MRREVIEWER = {Matja{\v{z}} Konvalinka},
}

@incollection {CSSkanHacq,
    AUTHOR = {Clearman, Sam and Shelton, Brittany and Skandera, Mark},
     TITLE = {Hecke algebra characters and quantum chromatic symmetric
              functions},
 BOOKTITLE = {24th {I}nternational {C}onference on {F}ormal {P}ower {S}eries
              and {A}lgebraic {C}ombinatorics ({FPSAC} 2012)},
    SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AR},
     PAGES = {551--562},
 PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
      YEAR = {2012},
   MRCLASS = {05E05},
  MRNUMBER = {2958028},
}

@incollection {CHSSkanEhatKL,
    AUTHOR = {Clearman, Sam and Hyatt, Matthew and Shelton, Brittany and Skandera, Mark},
     TITLE = {Evaluations of {H}ecke algebra traces at {K}azhdan-{L}usztig basis elements},
 BOOKTITLE = {25th {I}nternational {C}onference on {F}ormal {P}ower {S}eries
              and {A}lgebraic {C}ombinatorics ({FPSAC} 2013)},
    SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AU},
     PAGES = {1119--1130},
 PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
      YEAR = {2013},
}

@Unpublished{CHSSkanEhatKLbe,
    AUTHOR = {Clearman, Sam and Hyatt, Matthew and Shelton, Brittany and Skandera, Mark},
     TITLE = {Evaluations of {H}ecke algebra traces at {K}azhdan-{L}usztig basis elements},
    note =       "Preprint {math.CO/1502.04633v1} on {ArXiv}",
    year =	 2015
}

@article{CHSSkanEKL,
    AUTHOR = {Clearman, Samuel and Hyatt, Matthew and Shelton, Brittany and
              Skandera, Mark},
     TITLE = {Evaluations of {H}ecke algebra traces at {K}azhdan-{L}usztig
              basis elements},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {23},
      YEAR = {2016},
    NUMBER = {2},
      NOTE = {Paper 2.7, 56 pages},
   MRCLASS = {20C08 (05E05 05E10)},
  MRNUMBER = {3512629},
MRREVIEWER = {Michael Chmutov},
}


@book{SkanNIST,
  author = 	 "M. Skandera and M. Swanson",
  title = 	 "{User's Guide to the {NIST} Computer Security Bulletin 
                  Board System}",
  year =	 1991,
  number =       "NISTIR 4933",
  publisher =    "National Institute of Standards and Technology",
  address =      "Gaithersburg, MD"
}

		  		  		  
@unpublished{SkanResource,
  author = 	 "M. Skandera",
  title = 	 "Sources of information for researchers",
  year =	 2001,
  month =	 "September",
  note =         "following Section 1, in application for UROP Mini-Grant",
}

		  		  
@unpublished{SkanUROPProp,
  author = 	 "M. Skandera",
  title = 	 "UROP Research Plan",
  year =	 2000,
  month =	 "November",
  note =         "Section 1, application for UROP Mini-Grant"
}

		  
@unpublished{SkanUgDmcUROP,
  author = 	 "M. Skandera",
  title = 	 "On Permutations",
  year =	 2000,
  month =	 "November",
  note =         "manuscript following Section 1, in application for UROP Mini-Grant"
}

@unpublished{SkanUg31UROP,
  author = 	 "M. Skandera",
  title = 	 "Interval orders and related posets",
  year =	 2001,
  month =	 "September",
  note =         "manuscript following Section 1, in application for UROP Mini-Grant"
}

@unpublished{Skanlogc,
  author = 	 "M. Skandera",
  title = 	 "A note on polynomials with positive coefficients and
		  only real roots",
  year =	 2002,
  month =	 "June",
  note =         "working notes"
}

@article {SklyaninAlgStr,
    AUTHOR = {Sklyanin, E. K.},
     TITLE = {Some algebraic structures connected with the {Y}ang-{B}axter
              equation. {R}epresentations of a quantum algebra},
   JOURNAL = {Funktsional. Anal. i Prilozhen.},
  FJOURNAL = {Akademiya Nauk SSSR. Funktsional\cprime ny\u\i\ Analiz i ego
              Prilozheniya},
    VOLUME = {17},
      YEAR = {1983},
    NUMBER = {4},
     PAGES = {34--48},
   MRCLASS = {82A15 (22E70 58F07)},
}

@book {SmithInvitationAG,
    AUTHOR = {Smith, Karen E. and Kahanp{\"a}{\"a}, Lauri and
              Kek{\"a}l{\"a}inen, Pekka and Traves, William},
     TITLE = {An invitation to algebraic geometry},
    SERIES = {Universitext},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {2000},
     PAGES = {xii+155},
   MRCLASS = {14-01},
  MRNUMBER = {MR1788561 (2001k:14002)},
MRREVIEWER = {Gary P. Kennedy},
}

@incollection{SmythIneq,
    AUTHOR = {Smyth, C. J.},
     TITLE = {An inequality for polynomials},
 BOOKTITLE = {Number theory (Ottawa, ON, 1996)},
    SERIES = {CRM Proc. Lecture Notes},
    VOLUME = {19},
     PAGES = {315--321},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1999},
   MRCLASS = {11R80 (11C08)},
  MRNUMBER = {MR1684612 (2000d:11145)},
MRREVIEWER = {D. Boyd}
}
		  
@Article{SmythTPAI,
  author = 	 "C. J. Smyth",
  title = 	 "Totally positive algebraic integers of small trace",
  journal =	 "Ann. Inst. Fourier (Grenoble)",
  volume = 	 33,
  number =       3,
  pages =        "1--28",
  year =	 1984
}

@book {SnaithEBI,
    AUTHOR = {Snaith, Victor P.},
     TITLE = {Explicit {B}rauer Induction, With Applications to Algebra and Number Theory},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {40},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1994},
     PAGES = {xii+409},
   MRCLASS = {20C15 (11R33 11R42 11R65 19A31)},
  MRNUMBER = {1310780},
MRREVIEWER = {M. E. Keating},
       DOI = {10.1017/CBO9780511600746},
       URL = {https://doi.org/10.1017/CBO9780511600746},
}

@Article{Soergel,
  author = 	 "W. Soergel",
  title = 	 "{K}azhdan-{L}usztig polynomials and a combinatoric for tilting modules",
  journal =	 "Represent. Theory",
  volume = 	 1,
  pages =        "83--114 (electronic)",
  year =	 1997
}
		  
@article {SoibelmanFlag,
    AUTHOR = {So{\u\i}belman, Ya. S.},
     TITLE = {On the quantum flag manifold},
   JOURNAL = {Funktsional. Anal. i Prilozhen.},
  FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Funktsional\cprime ny\u\i\
              Analiz i ego Prilozheniya},
    VOLUME = {26},
      YEAR = {1992},
    NUMBER = {3},
     PAGES = {90--92},
   MRCLASS = {17B37 (14F05 17B10)},
  MRNUMBER = {MR1189033 (93k:17037)},
MRREVIEWER = {J. S. Joel},
}

@article{SolomonMackey,
    AUTHOR = {Solomon, Louis},
     TITLE = {A {M}ackey formula in the group ring of a {C}oxeter group},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {41},
      YEAR = {1976},
    NUMBER = {2},
     PAGES = {255--264},
}


@PhdThesis{song,
  author = 	 {Mingjie Song},
  title = 	 {Schubert Varieties in $S_p(2n)/B$},
  school = 	 {Northeastern},
  year = 	 1996,
  address =	 {Boston, MA},
  month =	 {May}
}

		  
@PhdThesis{song96,
  author = 	 "Mingjie Song",
  title = 	 "Schubert varieties in $Sp(2n)/B$",
  school = 	 "Northeastern University",
  year = 	 1996,
  address =	 "Boston, MA",
  month =	 "May"
}

		  
		  
@Article{sottile,
  author = 	 "Frank Sottile",
  title = 	 "{Pieri's} formula for flag manifolds and {Schubert} polynomial",
  journal =	 "Ann. Inst. Fourier",
  year =	 1996,
  volume =	 46,
  number =	 1,
  pages =	 "89--110"
}


@article{SpeyerWillTrop,
    AUTHOR = {Speyer, David and Williams, Lauren},
     TITLE = {The tropical totally positive {G}rassmannian},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {22},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {189--210},
     CODEN = {JAOME7},
   MRCLASS = {14P99 (05E25 14M15)},
  MRNUMBER = {MR2164397 (2006e:14084)},
MRREVIEWER = {Meirav Amram-Blei},
}

@article{Springer,
  author = 	 "T. A. Springer",
  title = 	 "Quelques applications de la cohomologie d'intersection",
  journal =	 "Ast\'erisque",
  year =	 1982,
  volume =	 "92-93",
  pages =	 "249-273",
  note =	 "Bourbaki Seminar, Col 1981/1982"
}		  

		  
@Incollection{SpringerQACI,
  author = 	 "T. A. Springer",
  title = 	 "Quelques aplications de la cohomologie d'intersection",
  booktitle =	 "S\'eminaire Bourbaki, Vol.\,1981/1982",
  series =	 "Ast{\'e}risque",
  year =	 1982,
  volume =	 92,
  publisher =    "Soc. Math. France",
  address =      "Paris",
  pages =	 "249--273"
}

@article {SraIneq,
    AUTHOR = {Sra, Suvrit},
     TITLE = {On inequalities for normalized {S}chur functions},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {51},
      YEAR = {2016},
     PAGES = {492--494},
   MRCLASS = {05E05},
  MRNUMBER = {3398873},
       DOI = {10.1016/j.ejc.2015.07.005},
       URL = {https://doi.org/10.1016/j.ejc.2015.07.005},
}

@Article{stankova94,
  author = 	 "Z. Stankova",
  title = 	 "Forbidden Subsequences",
  journal =	 "Discrete Math.",
  year =	 1994,
  volume =	 132,
  pages =	 "291--316"
}

@Article{S1,
  author = 	 "R. Stanley",
  title = 	 "Theory and application of plane partitions, Parts 1
		  and 2",
  journal =	 "Studies in Applied Math",
  year =	 1971,
  volume =	 50,
  pages =	 "167--188, 259--279"
}

@Incollection{StanPos,
  author = 	 "R. Stanley",
  title = 	 "Positivity problems and conjectures",
  booktitle =    "Mathematics: Frontiers and Perspectives", 
  publisher =    "American Mathematical Society",
  address =      "Providence, RI",		  
  editor =       "V. Arnold and M. Atiyah and P. Lax and B. Mazur", 
  year =	 "2000",
  pages =        "295--319"
}
		  
@Article{StanSymm,
  author = 	 "R. Stanley",
  title = 	 "{A symmetric function generalization of the chromatic
                   polynomial of a graph}",
  journal =	 "Adv. Math.",
  year =	 1995,
  volume =	 111,
  pages =	 "166--194"
}

@Article{StanStemIJT,
  author = 	 "R. Stanley and J. R. Stembridge",
  title = 	 "{On immanants of Jacobi-Trudi matrices and 
                   permutations with restricted positions}",
  journal =	 "J. Combin. Theory Ser. A",
  year =	 1993,
  volume =	 62,
  pages =	 "261--279"
}

@Article{S2,
  author = 	 "R. Stanley",
  title = 	 "{Ordered structures and partitions}",
  journal =	 " Memoirs  Amer.\  Math.\  Soc.",
  year =	 1972,
  number =	 119,
  note =	 "American Mathematical Society, Providence, RI"
}

@Article{StanAnti,
  author = 	 "R. Stanley",
  title = 	 "{A matrix for counting paths in acyclic digraphs}",
  journal =	 "J. Combin. Theory Ser. A",
  year =	 1996,
  volume =	 74,
  pages =	 "169--172"
}

@Incollection{StanCMC,
  author = 	 "R. Stanley",
  title = 	 "{Cohen-Macaulay} Complexes",
  editor =       "M. Aigner",
  year =	 1977,
  booktitle =    "Higher Combinatorics",
  volume =	 19,
  publisher =    "D. Reidel Publishing Company",
  address =      "Dordrecht-Holland",
  pages =	 "51--62"
}
		  		  
@Article{StanBCMC,
  author = 	 "R. Stanley",
  title = 	 "Balanced {Cohen-Macaulay} Complexes",
  journal =	 "Trans. Amer. Math. Soc.",
  year =	 1979,
  volume =	 241,
  number =	 1,
  pages =	 "139--157"
}

@Article{StanAG,
  author = 	 "R. Stanley",
  title = 	 "{Graph colorings And Related Symmetric functions:
                   Ideas and Applications}",
  journal =	 "Discrete Math.",
  year =	 1998,
  volume =	 193,
  pages =	 "267--286"
}


@InCollection{S5,
  author = 	 "R. P. Stanley",
  title = 	 "{Some combinatorial aspects of the Schubert calculus}",
  booktitle =	 "Combinatoire et Repr\'esentation du Groupe Sym\'etrique",
  publisher =	 "Springer Lecture Notes in Math",
  year =	 1977,
  editor =	 "D.~Foata",
  volume =	 579,
  pages =	 "217--251",
  address =	 "Strasbourg"
}


@InCollection{StanLog,
  author = 	 "R. Stanley",
  title = 	 "Log-Concave and Unimodal Sequences in Algebra, Combinatorics, and Geometry",
  booktitle =	 "Graph Theory and its Applications: East and West",
  publisher =	 "Annals of the New York Academy of Sciences",
  month =        "December 29,", 
  year =	 1989,
  volume =	 576,
  pages =	 "500--535"
}


@Article{S3,
  author = 	 "R. Stanley",
  title = 	 "{On the number of reduced decompositions
of elements of Coxeter groups}",
  journal =	 "Europ. J. Combin.",
  year =	 1984,
  volume =	 5,
  pages =	 "359--372"
}


@Article{S6,
  author = 	 "R. Stanley",
  title = 	 "{Unimodality and Lie Superalgebras}",
  journal =	 "Studies in Applied Mathematics",
  year =	 1985,
  volume =	 72,
  pages =	 "263--281"
}


@Book{StanEC1,
  author = 	 "R. Stanley",
  title = 	 "{Enumerative Combinatorics}",
  publisher = 	 "Cambridge University Press",
  year = 	 1997,
  volume =	 1,
  address =      "Cambridge"		  
}

@Book{StanEC2,
  author = 	 "R. Stanley",
  title = 	 "{Enumerative Combinatorics}",
  publisher = 	 "Cambridge University Press",
  year = 	 1999,
  address =      "Cambridge",		  
  volume =	 2
}

@Book{StanCCA,
  author = 	 "R. Stanley",
  title = 	 "{Combinatorics and Commutative Algebra}",
  publisher = 	 "Birkh{\"a}user",
  year = 	 1996,
  address =	 "Boston, MA"
}

@Article{S7,
  author = 	 "Richard P. Stanley",
  title = 	 "Weyl Groups, the Hard {Lefschetz} Theorem, and the
		  {Sperner} property",
  journal =	 "SIAM J. Alg. Disc. Meth.",
  year =	 1980,
  volume =	 1,
  number =	 2,
  pages =	 "168--184"
}


@Article{S8,
  author = 	 "Richard Stanley",
  title = 	 "Quotients of {Peck} Posets",
  journal =	 "Order",
  year =	 1984,
  volume =	 1,
  pages =	 "29-34"
}

@Article{StanMono,
  author = 	 "Richard Stanley",
  title = 	 "A monotonicity property of $h$-vectors and
		  $h^*$-vectors",
  journal =	 "Europ. J. Combin.",
  year =	 1993,
  volume =	 14,
  pages =	 "251-258"
}
		  
@PhdThesis{StanThesis,
  author = 	 "R. Stanley",
  title = 	 "Ordered Structures and Partitions",
  school = 	 "Harvard University",
  year = 	 1971
}

@Book{Stein,
  author = 	 "R. Steinberg",
  title = 	 "{Lectures on Chevalley Groups}",
  publisher = 	 "Yale University press",
  year = 	 1967,
  address =	 "New Haven, Conn."
}

@PhdThesis{EinarThesis,
  author = 	 "Einar {Steingr\'\i msson}",
  title = 	 "{Permutation Statistics of Indexed and Poset Permutations}",
  school = 	 "MIT",
  year = 	 1992,
  address =	 "Cambridge, MA"
}


@unpublished{StemOrdRep,
    AUTHOR = {Stembridge, John R.},
     TITLE = {Ordinary representations of {$B_n$}},
      NOTE = {Unpublished manuscript},
}

@article {StemProjRep,
    AUTHOR = {Stembridge, John R.},
     TITLE = {The projective representations of the hyperoctahedral group},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {145},
      YEAR = {1992},
    NUMBER = {2},
     PAGES = {396--453},
   MRCLASS = {20C25},
  MRNUMBER = {1144940},
MRREVIEWER = {A. O. Morris},
       DOI = {10.1016/0021-8693(92)90110-8},
       URL = {https://doi.org/10.1016/0021-8693(92)90110-8},
}

@unpublished {StemCounter,
  author = 	 "John Stembridge",
  title = 	  "Counterexamples to the {Poset Conjecture}",
  note =	 "To appear in {\em Trans. Amer. Math. Soc.}",
  year =	 2004
}

@Article{StemRed,
  author = 	 "John Stembridge",
  title = 	  "Some combinatorial aspects of reduced words in 
                    finite {Coxeter} groups",
  journal =	 "Trans. Amer. Math. Soc.",
  volume =	 349,
  pages =	 {1285--1332},
  year =	 1997
}

@Article{StemConj,
  author = 	 "John R. Stembridge",
  title = 	 "Some conjectures for immanants",
  journal =	 "Canad.\ J.\ Math.",
  volume =	 44,
  number =       5,
  pages =	 {1079--1099},
  year =	 1992
}

@Article{StemImm,
  author = 	 "John Stembridge",
  title = 	 "Immanants of Totally Positive Matrices are Nonnegative",
  journal =	 "Bull. London Math. Soc.",
  volume =	 23,
  pages =	 {422--428},
  year =	 1991
}

@Article{StemMultFreeSchur,
  author = 	 "John Stembridge",
  title = 	 "Multiplicity-free products of {Schur} functions",
  journal =	 "Ann. Comb.",
  volume =	 5,
  pages =	 {113--121},
  year =	 2001
}

@Unpublished{Stem1,
  author = 	 "John Stembridge",
  note = 	 "personal communication",
  year =	 1993
}

@Unpublished{Stem2,
  author = 	 "John Stembridge",
  title = 	 "{Coxeter-Yang-Baxter Equations}",
  note = 	 "Manuscript",
  year =	 1993,
  month =	 "February"
}
		  
@Unpublished{StemLecRepn,
  author = 	 "John Stembridge",
  title = 	 "Lectures on Combinatorics and Group Representations",
  note = 	 "Unpublished lecture notes",
  year =	 2000
}		  

@Misc{StemComm,
  author = 	 "John Stembridge",
  year =         "2004",
  note = 	 "Personal communication"
}


@Book{Stein,
  author = 	 "R. Steinberg",
  title = 	 "{Lectures on Chevalley Groups}",
  publisher = 	 "Yale University press",
  year = 	 1967,
  address =	 "New Haven, Conn."
}

		  
@article{SunWagWest,
  author = 	 "T. S. Sundquist and D. G. Wagner and J.West",
  title = 	 "A {Robinson}-{Schensted} algorithm for a class of partial orders",
  journal =	 "J. Combin. Theory Ser. A",
  year =	 1997,
  volume =	 79,
  pages =	 "36--52"
}

@book{Sweedler,
    AUTHOR = {Sweedler, Moss E.},
     TITLE = {Hopf algebras},
    SERIES = {Mathematics Lecture Note Series},
 PUBLISHER = {W. A. Benjamin, Inc., New York},
      YEAR = {1969},
     PAGES = {vii+336},
   MRCLASS = {18.20 (16.00)},
  MRNUMBER = {0252485 (40 \#5705)},
MRREVIEWER = {K.-T. Chen},
}

@unpublished {TamvakisAmenable,
    AUTHOR = {Tamvakis, Harry},
     TITLE = {Degeneracy locus formulas for amenable {Weyl} group elements},
    NOTE = {Preprint {\tt math.AG:1909.06398} on {ArXiv}},
    YEAR = {2019},
}


@article {TanisakiBB,
    AUTHOR = {Tanisaki, Toshiyuki},
     TITLE = {The {B}eilinson-{B}ernstein correspondence for quantized
              enveloping algebras},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {250},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {299--361},
       URL = {http://dx.doi.org/10.1007/s00209-004-0754-9},
}

@article {TanisakiFDRQG,
    AUTHOR = {Tanisaki, Toshiyuki},
     TITLE = {Finite-dimensional representations of quantum groups},
   JOURNAL = {Osaka J. Math.},
  FJOURNAL = {Osaka Journal of Mathematics},
    VOLUME = {28},
      YEAR = {1991},
    NUMBER = {1},
     PAGES = {37--53},
       URL = {http://projecteuclid.org/getRecord?id=euclid.ojm/1200782857},
}
				

@article {TaskOrders,
    AUTHOR = {Ta{\c{s}}kin, M{\"u}ge},
     TITLE = {Properties of four partial orders on standard {Y}oung
              tableaux},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {113},
      YEAR = {2006},
    NUMBER = {6},
     PAGES = {1092--1119}
}


@Incollection{TitsMots,
  author = 	 "J. Tits",
  title = 	 "Le probl\`eme des mots dans les groupes de {Coxeter}",
  booktitle =	 "Symposia Mathematica (INDAM, Rome, 1967/68), Vol.\ 1",
  year =	 1969,
  volume =	 1,
  pages =	 "175-185",
  publisher =    "Academic Press",
  address =      "London"
}

@Article{TW97,
  author = 	 "S. Tolman and J. Weitsman",
  title = 	 "The Cohomology Ring of Abelian Symplectic Quotients",
  journal =	 "preprint",
  year =	 1997
}

@Book{Trott,
  author = 	 "W. T. Trotter",
  title = 	 "Combinatorics and Partially Ordered Sets: Dimension Theory",
  publisher = 	 "Johns Hopkins University Press",
  address =	 "Baltimore",
  year = 	 1992
}

@article {Ty2,
    AUTHOR = {Tymoczko, Julianna S.},
     TITLE = {Permutation representations on {S}chubert varieties},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {130},
      YEAR = {2008},
    NUMBER = {5},
     PAGES = {1171--1194},
   MRCLASS = {14M15 (14F25 14F43)},
  MRNUMBER = {2450205},
MRREVIEWER = {Harry Tamvakis},
       DOI = {10.1353/ajm.0.0018},
       URL = {https://doi.org/10.1353/ajm.0.0018},
}

@incollection {Ty3,
    AUTHOR = {Tymoczko, Julianna S.},
     TITLE = {Permutation actions on equivariant cohomology of flag
              varieties},
 BOOKTITLE = {Toric topology},
    SERIES = {Contemp. Math.},
    VOLUME = {460},
     PAGES = {365--384},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2008},
   MRCLASS = {14M15 (14N15 20C30 55N91)},
  MRNUMBER = {2428368},
MRREVIEWER = {Christian Ohn},
       DOI = {10.1090/conm/460/09030},
       URL = {https://doi.org/10.1090/conm/460/09030},
}
		

@Article{vdH,
  author = 	 "A. van den Hombergh",
  title = 	 "{Note on a paper by Bernstein, Gelfand, Gelfand on
		  Verma modules}",
  journal =	 "Proc. Konin. Neder. Aka.Amsterddam Ser. A",
  year =	 1974,
  volume =	 77,
  pages =	 "352-356"
}

@misc{VLRS,
  author =       "M. van Leeuwen", 
  title =        "The {Robinson-Schensted} and {Sch\"utzenberger} algorithms,
part {II}: geometric interpretations",
  note =         "CWI report AM-R9209",
  year =         "1992"
}

@article{vWEquality,
    AUTHOR = {van Willigenburg, Stephanie},
     TITLE = {Equality of {S}chur and skew {S}chur functions},
   JOURNAL = {Ann. Comb.},
  FJOURNAL = {Annals of Combinatorics},
    VOLUME = {9},
      YEAR = {2005},
    NUMBER = {3},
     PAGES = {355--362},
   MRCLASS = {05E05 (05E10)},
  MRNUMBER = {MR2176598 (2006e:05183)},
MRREVIEWER = {Grant Walker},
}


@article {vWCoincidence,
    AUTHOR = {Reiner, Victor and Shaw, Kristin M. and van Willigenburg,
              Stephanie},
     TITLE = {Coincidences among skew {S}chur functions},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {216},
      YEAR = {2007},
    NUMBER = {1},
     PAGES = {118--152},
}

@article {VanderAlg,
    AUTHOR = {Van der Jeugt, J.},
     TITLE = {An algorithm for characters of {H}ecke algebras {$H_n(q)$}
              of type {$A_{n-1}$}},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {24},
      YEAR = {1991},
    NUMBER = {15},
     PAGES = {3719--3725},
     CODEN = {JPHAC5},
   MRCLASS = {05E10 (05A30 16G99 20C15 81R05)},
  MRNUMBER = {1123644},
MRREVIEWER = {Richard Dipper},
       URL = {http://stacks.iop.org/0305-4470/24/3719},
}

@article {VJIdPer,
    AUTHOR = {Vere-Jones, D.},
     TITLE = {An identity involving permanents},
   JOURNAL = {Linear Algebra Appl.},
  FJOURNAL = {Linear Algebra and its Applications},
    VOLUME = {63},
      YEAR = {1984},
     PAGES = {267--270},
}
		

@article {VJPDBF,
    AUTHOR = {Vere-Jones, D.},
     TITLE = {Permanents, determinants, bosons and fermions},
   JOURNAL = {New Zealand Math. Soc. Newslett.},
  FJOURNAL = {New Zealand Mathematical Society Newsletter},
    VOLUME = {29},
      YEAR = {1983},
     PAGES = {18--23},
}
		
@Article{Ve1,
  author = 	 "D.-N. Verma",
  title = 	 "Structure of certain induced representations of
		  complex semisimple Lie algebras",
  journal =	 "Bull. Amer. Math. Soc.",
  year =	 1968,
  volume =	 74,
  pages =	 "160-166"
}


@Article{Wachs,
  author = 	 "M.L. Wachs",
  title = 	 "{Flagged Schur functions, Schubert polynomials, and
		  symmetrizing operators}",
  journal =	 "J.  Combin. Theory Ser. A",
  year =	 1985,
  volume =	 40,
  pages =	 "276--289"
}


@Article{WagEnum,
  author = 	 "D. Wagner",
  title =        "Enumeration of functions from posets to chains", 
  journal =	 "Europ. J. Combin.",
  year = 	 1992,
  volume =	 13,
  pages =	 "313--324"
}

@Misc{WarComm,
  author = 	 "G. Warrington",
  note = 	 "Personal communication",
  year =	 2002
}
		  
@article{WWXOptics,
    AUTHOR = {Wei, L. F. and Wang, S. J. and Xi, D. P.},
     TITLE = {Inverse $q$-boson operators and their relation to photon-added and photon-depleted states},
   JOURNAL = {J. Opt. B Quantum Semiclass. Opt.},
  FJOURNAL = {Journal of Optics B. Quantum and Semiclassical Optics},
    VOLUME = {1},
      YEAR = {1999},
    NUMBER = {6},
     PAGES = {619--623},
      ISSN = {1464-4266}
}

		  
@Book{Welsh,
  author = 	 "D. Welsh",
  title = 	 "{Matroid Theory}",
  publisher = 	 "Academic Press",
  year = 	 1976
}

@Book{WestGT,
  author = 	 "D. West",
  title = 	 "{Introduction to Graph Theory}",
  publisher = 	 "Prentice Hall",
  year = 	 1996
}

		  
@PhdThesis{west,
  author = 	 "Julian West",
  title =  "{Permutations with forbidden sequences; and, stack-sortable permutations}", 
  school = 	 "MIT",
  year = 	 1990
}

@Article{WestburyTL,
  author = 	 "B. W. Westbury",
  title = 	 "The representation theory of the {Temperley-Lieb} algebras", 
  journal =	 "Math. Z.",
  volume =       219,
  pages =        "539--565",
  year =	 1995
}


@Article{WReduction,
  author = 	 "A. Whitney",
  title = 	 "A reduction theorem for totally positive matrices",
  journal =	 "J. Anal. Math.",
  volume =       2,
  pages =        "88-92",
  year =	 1952
}

@Article{HWhitneyAbstract,
  author = 	 "H. Whitney",
  title = 	 "On the abstract properties of linear dependence",
  journal =	 "Amer. J. Math.",
  volume =       57,
  pages =        "509--533",
  year =	 1935
}

@Article{WienerCTRP,
  author = 	 "N. Wiener",
  title = 	 "A contribution to the theory of relative position",
  journal =	 "Proc.\ Cambridge Philos.\ Soc.",
  year =	 1914,
  volume =	 17,
  pages =	 "441--449"
}


@article {WilliamsETPGrass,
    AUTHOR = {Williams, Lauren K.},
     TITLE = {Enumeration of totally positive {G}rassmann cells},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {190},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {319--342},
     CODEN = {ADMTA4},
   MRCLASS = {05E15 (05A15 14M15)},
  MRNUMBER = {MR2102660 (2005i:05197)},
MRREVIEWER = {Gregory S. Warrington},
}
		  
@Article{WF,
  author = 	 "R. L. Wine and J. E. Freund",
  title = 	 "On the enumeration of decision patterns involving $n$ means",
  journal =	 "Ann. Math. Stat.",
  volume =       28,
  pages =        "256--259",
  year =	 1957
}

@Article{W1,
  author = 	 "Rudolf Winkel",
  title = 	 "On the multiplication of {Schubert} polynomials",
  journal =	 "preprint",
  year =	 1996
}

@Article{W2,
  author = 	 "Rudolf Winkel",
  title = 	 "A combinatorial rule for the generation of
		  {Schubert} polynoimals",
  journal =	 "preprint",
  year =	 1996
}

@book{WolfgangThesis,
    AUTHOR = {Wolfgang, III, Harry Lewis},
     TITLE = {Two interactions between combinatorics and representation
              theory: {M}onomial immanants and {H}ochschild cohomology},
      NOTE = {Thesis (Ph.D.)--Massachusetts Institute of Technology},
 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {1997},
     PAGES = {(no paging)},
   MRCLASS = {Thesis},
  MRNUMBER = {2716737},
       URL = {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:0598665},
}



@PhdThesis{Worley,
  author = 	 "D. R. Worley",
  title = 	 "{A theory of shifted Young tableaux}",
  school = 	 "MIT",
  year = 	 1984
}



@article {ZaslavskySGC,
    AUTHOR = {Zaslavsky, T},
     TITLE = {Signed graph coloring},
   JOURNAL = {Discrete Math.},
    VOLUME = {39},
      YEAR = {1982},
     PAGES = {215--228}
}


@article {ZelSmallRes,
    AUTHOR = {Zelevinski{\u\i}, A. V.},
     TITLE = {Small resolutions of singularities of {S}chubert varieties},
   JOURNAL = {Funktsional. Anal. i Prilozhen.},
    VOLUME = {17},
      YEAR = {1983},
    NUMBER = {2},
     PAGES = {75--77}
}

@Inproceedings{ZelLR3,
  author = 	 "A. Zelevinsky",
  title = 	 "From {Littlewood-Richardson} coefficients to 
                  cluster algebras in three lectures",
  year =	 2002,
  editor =       "S. Fomin",
  booktitle =    "Symmetric Functions 2001: Surveys of 
                  Developments and Perspectives",
  series =       "NATO Science Series II: Mathematics, Physics, 
                  and Chemistry",
  volume =       "74",
  publisher =    "Kluwer",
  address =      "Dordrecht",
  pages =	 "253--273"
}		  

@article {JZhangqCHT,
    AUTHOR = {Zhang, J. J.},
     TITLE = {The quantum {C}ayley-{H}amilton theorem},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {129},
      YEAR = {1998},
    NUMBER = {1},
     PAGES = {101--109},
}

@article {HZhangDCB,
    AUTHOR = {Zhang, Hechun},
     TITLE = {On dual canonical bases},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {37},
      YEAR = {2004},
    NUMBER = {32},
     PAGES = {7879--7893},
     CODEN = {JPHAC5},
   MRCLASS = {17B37 (81R50)},
}
		
@article {ZhangHowe,
    AUTHOR = {Zhang, R. B.},
     TITLE = {Howe duality and the quantum general linear group},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {131},
      YEAR = {2003},
    NUMBER = {9},
     PAGES = {2681--2692},
   MRCLASS = {17B37},
  MRNUMBER = {1974323},
MRREVIEWER = {Vladislav K. Kharchenko},
       URL = {https://doi.org/10.1090/S0002-9939-02-06892-2},
}


@unpublished{ZhaoTNN,
  author = 	 "Brian Zhao",
  title = 	 "Total non-negativity: the relation to matrices and 
polynomials",
  year =	 2004,
  note =         "unpublished REU paper"
}
 
@Article{ZChess,
  author = 	 "G. Ziegler",
  title = 	 "Shellability of Chessboard Complexes",
  journal =	 "Isr. J. Math.",
  year =	 1994,
  volume =	 87,
  pages =	 "97-110"
}

@Unpublished{SkanCCSv1,
    AUTHOR = {Skandera, Mark},
    TITLE = {Characters and chromatic symmetric functions},
    NOTE = {Preprint {math.CO/2010.00458v1} on {ArXiv}},
    year =	 2020
}
%Preprint {math.CO/1502.04633v1} on {ArXiv}",

@Unpublished{SkanGCEHGC,
    AUTHOR = {Skandera, Mark},
     TITLE = {Graph coloring and hyperoctahedral group character evaluations},
    note =  "In preparation",
    year =  2023
}

@Unpublished{SkanBCDefect,
    AUTHOR = {Skandera, Mark},
     TITLE = {A defect formula for multiplication of {Kazhdan--Lusztig}
     basis elements of the type-{$\mathsf{BC}$} {Hecke} algebra},
    note =  "In preparation",
    year =  2023
}

@misc{SkanSoskinBJArx,
    AUTHOR = {Skandera, Mark and Soskin, Daniel},
EPRINT = {2209.06466},
EPRINTTYPE = {arxiv},
     TITLE = {{Barrett}--{Johnson} inequalities for totally nonnegative matrices},
    year =	 {2022}
}

@Unpublished{SkanSoskinBRPerm,
    AUTHOR = {Skandera, Mark and Soskin, Daniel},
     TITLE = {Bounded permanental ratios for totally nonnegative matrices},
    NOTE = {In preparation},
    year =  2023
}


%manual{SkanIntroalt,
%  author = 	 "M. Skandera",
%  title = 	 "{Introduction to Combinatorics and Graph Theory}",
%  year =	 2002,
%  note =         "Unpublished lecture notes" 
%for {U. Michigan} course
%		  {Math} 565"	   
%}

%Unpublished{LPPSNN,
%  author = 	 "Thomas Lam and Alexander Postnikov and Pavlo Pylyavskyy",
%  title = 	 "Schur positivity and {Schur} log-concavity",
%  note =         "Preprint {math.CO/0502446} on {ArXiv}",
%  year =	 2005
%}
%# On tensor products of polynomial representations (with Kevin Purbhoo), preprint (2006)