@PhDThesis{Vivianethese,
	title = {Combinatoire alg\'ebrique li\'ee aux ordres sur les permutations},
	author = {Pons, V.},
	school = {Universit\'e Paris-Est Marne-la-Vall\'ee},
	year = {2013},
	type={{T}h\`ese de {D}octorat},

ARXIV = {1310.1805},
SLIDES = {soutenance_these.pdf}
}


@Article{	  Demazure.1974,
  author	= {Demazure, Michel},
  title		= {D\'esingularisation des vari\'et\'es de {S}chubert
		  g\'en\'eralis\'ees},
  note		= {Collection of articles dedicated to Henri Cartan on the
		  occasion of his 70th birthday, I},
  journal	= {Ann. Sci. \'Ecole Norm. Sup. (4)},
  fjournal	= {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
		  Quatri\`eme S\'erie},
  volume	= {7},
  year		= {1974},
  pages		= {53--88},
  issn		= {0012-9593},
  mrclass	= {14M15 (20G05)},
  mrnumber	= {0354697 (50 \#7174)},
  mrreviewer	= {S. I. Gelfand}
}

@InCollection{	  Lascoux.2001,
  author	= {Lascoux, A.},
  title		= {Transition on {G}rothendieck polynomials},
  booktitle	= {Physics and combinatorics, 2000 ({N}agoya)},
  pages		= {164--179},
  publisher	= {World Sci. Publ., River Edge, NJ},
  year		= {2001},
  mrclass	= {14M15 (05E05 19E08)},
  mrnumber	= {1872255 (2002k:14082)},
  mrreviewer	= {Frank Sottile}
}

@Article{	  Lascoux.2003.slc,
  author	= {Lascoux, Alain},
  title		= {Schubert \& {G}rothendieck: un bilan bid\'ecennal},
  journal	= {S\'em. Lothar. Combin.},
  fjournal	= {S\'eminaire Lotharingien de Combinatoire},
  volume	= {50},
  year		= {2003/04},
  pages		= {Art. B50i, 32 pp. (electronic)},
  issn		= {1286-4889},
  mrclass	= {05E15 (05E05 14M15 14N15)},
  mrnumber	= {2118047 (2005j:05099)},
  mrreviewer	= {Harry Tamvakis}
}

@book {FlajoletSedgewick.2009,
    AUTHOR = {Flajolet, Philippe and Sedgewick, Robert},
     TITLE = {Analytic combinatorics},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2009},
     PAGES = {xiv+810},
      ISBN = {978-0-521-89806-5},
   MRCLASS = {05-02 (05A15 05A16 60C05 60E10 82-01)},
  MRNUMBER = {2483235 (2010h:05005)},
       DOI = {10.1017/CBO9780511801655},
       URL = {http://dx.doi.org/10.1017/CBO9780511801655},
}

@book {CurtisReiner.1990,
    AUTHOR = {Curtis, Charles W. and Reiner, Irving},
     TITLE = {Methods of representation theory. {V}ol. {I}},
    SERIES = {Wiley Classics Library},
      NOTE = {With applications to finite groups and orders,
              Reprint of the 1981 original,
              A Wiley-Interscience Publication},
 PUBLISHER = {John Wiley \& Sons, Inc., New York},
      YEAR = {1990},
     PAGES = {xxiv+819},
      ISBN = {0-471-52367-4},
   MRCLASS = {20-02 (01A75 11R33 20Cxx)},
  MRNUMBER = {1038525 (90k:20001)},
}

@Article{Green.1951,
  author	= {Green, J. A.},
  title		= {On the structure of semigroups},
  journal	= {Ann. of Math. (2)},
  fjournal	= {Annals of Mathematics. Second Series},
  volume	= {54},
  year		= {1951},
  pages		= {163--172},
  issn		= {0003-486X},
  mrclass	= {09.1X},
  mrnumber	= {MR0042380 (13,100d)},
  mrreviewer	= {J. Riguet}
}

@article {Renner.1995,
    AUTHOR = {Renner, Lex E.},
     TITLE = {Analogue of the {B}ruhat decomposition for algebraic monoids.
              {II}. {T}he length function and the trichotomy},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {175},
      YEAR = {1995},
    NUMBER = {2},
     PAGES = {697--714},
     CODEN = {JALGA4},
   MRCLASS = {20G99 (20M10)},
  MRNUMBER = {1339663},
MRREVIEWER = {Mohan S. Putcha},
}

@article {CanRenner.2012,
    AUTHOR = {Can, Mahir Bilen and Renner, Lex E.},
     TITLE = {Bruhat-{C}hevalley order on the rook monoid},
   JOURNAL = {Turk J. Math},
  FJOURNAL = {Turkinsh Journal of Mathematics},
    VOLUME = 36,
      YEAR = 2012,
    NUMBER = 2,
     PAGES = {499-519},
}

@online{OEIS,
    author = {Sloane, Neil J. A.},
        title = {{The On-Line Encyclopedia of Integer Sequences Foundation Inc}},
        year = 2015,
        url = {http://oeis.org},
        urldate = {2015-07-15}
}

@article {Iwahori.1964,
    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 IA. Mathematics},
    VOLUME = {10},
      YEAR = {1964},
     PAGES = {215--236 (1964)},
   MRCLASS = {20.75 (20.80)},
  MRNUMBER = {0165016},
MRREVIEWER = {Rimhak Ree},
}


@article {Solomon.1990,
    AUTHOR = {Solomon, Louis},
     TITLE = {The {B}ruhat decomposition, {T}its system and {I}wahori ring
              for the monoid of matrices over a finite field},
   JOURNAL = {Geom. Dedicata},
  FJOURNAL = {Geometriae Dedicata},
    VOLUME = {36},
      YEAR = {1990},
    NUMBER = {1},
     PAGES = {15--49},

     CODEN = {GEMDAT},
   MRCLASS = {20G40 (20M25)},
  MRNUMBER = {1065211},
MRREVIEWER = {Lex Renner},
}

@article {Solomon.2004,
    AUTHOR = {Solomon, Louis},
     TITLE = {The {I}wahori algebra of {$\textbf{M}_n(\textbf{F}_q)$}. {A}
              presentation and a representation on tensor space},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {273},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {206--226},
     CODEN = {JALGA4},
   MRCLASS = {20C08 (20M20)},
  MRNUMBER = {2032457},
MRREVIEWER = {Meinolf Geck},
}

@book {FultonHarris.1991,
    AUTHOR = {Fulton, William and Harris, Joe},
     TITLE = {Representation theory},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {129},
      NOTE = {A first course,
              Readings in Mathematics},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {1991},
     PAGES = {xvi+551},
      ISBN = {0-387-97527-6; 0-387-97495-4},
   MRCLASS = {20G05 (17B10 20G20 22E46)},
  MRNUMBER = {1153249},
MRREVIEWER = {James E. Humphreys},
       URL = {https://doi.org/10.1007/978-1-4612-0979-9},
}

@Article{LascouxSchutzenberger.1987,
author="Lascoux, A. and Sch{\"u}tzenberger, M. P.",
title="Symmetrization operators on polynomial rings",
journal="Functional Analysis and Its Applications",
year="1987",
volume="21",
number="4",
pages="324--326",
issn="1573-8485",
doi="10.1007/BF01077811",
url="https://doi.org/10.1007/BF01077811"
}


@book{Lascoux.2003.book,
  title={Symmetric Functions and Combinatorial Operators on Polynomials},
  author={Lascoux, A.},
  number={99},
  isbn={9780821828717},
  lccn={2003066740},
  series={Conference board of the Mathematical Sciences regional conference series in mathematics},
  url={https://books.google.de/books?id=RVj6MAAACAAJ},
  year={2003},
  publisher={American Mathematical Society}
}

@article {Halverson.2004,
    AUTHOR = {Halverson, Tom},
     TITLE = {Representations of the {$q$}-rook monoid},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {273},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {227--251},
     CODEN = {JALGA4},
   MRCLASS = {20C08 (17B37 20M20)},
  MRNUMBER = {2032458},
MRREVIEWER = {Dongho Moon},
}


@article{NCSF,
title = "Noncommutative Symmetrical Functions",
journal = "Advances in Mathematics",
volume = "112",
number = "2",
pages = "218 - 348",
year = "1995",
issn = "0001-8708",
doi = "https://doi.org/10.1006/aima.1995.1032",
url = "http://www.sciencedirect.com/science/article/pii/S0001870885710328",
author = "I.M. Gelfand and D. Krob and A. Lascoux and B. Leclerc and V.S. Retakh and J.Y. Thibon"
}

@Article{	  DuchampHivertThibon.2002,
  author	= {Duchamp, G{\'e}rard and Hivert, Florent and Thibon,
		  Jean-Yves},
  title		= {Noncommutative symmetric functions. {VI}. {F}ree
		  quasi-symmetric functions and related algebras},
  journal	= {Internat. J. Algebra Comput.},
  fjournal	= {International Journal of Algebra and Computation},
  volume	= {12},
  year		= {2002},
  number	= {5},
  pages		= {671--717},
  issn		= {0218-1967},
  mrclass	= {05E05},
  mrnumber	= {1 935 570}
}

@Book{BjornerBrenti.2005,
  author	= {Bj{\"o}rner, Anders and Brenti, Francesco},
  title		= {Combinatorics of {C}oxeter groups},
  series	= {Graduate Texts in Mathematics},
  volume	= {231},
  publisher	= {Springer},
  address	= {New York},
  year		= {2005},
  pages		= {xiv+363},
  isbn		= {978-3540-442387; 3-540-44238-3},
  mrclass	= {05-01 (05E15 20F55)},
  mrnumber	= {MR2133266 (2006d:05001)},
  mrreviewer	= {Jian-yi Shi}
}

@Book{Steinberg.2016,
  author	= {Steinberg, Benjamin},
  title		= {Representation Theory of Finite Monoids},
  series	= {Universitext},
  publisher	= {Springer},
  address	= {New York},
  year		= {2016},
  isbn		= {978-3-319-43930-3},
}

@article {DHST,
    AUTHOR = {Denton, Tom and Hivert, Florent and Schilling, Anne and
              Thi{\'e}ry, Nicolas M.},
     TITLE = {On the representation theory of finite $\mathcal{J}$-trivial
              monoids},
   JOURNAL = {S\'em. Lothar. Combin.},
  FJOURNAL = {S\'eminaire Lotharingien de Combinatoire},
    VOLUME = {64},
      YEAR = {2010/11},
     PAGES = {Art. B64d, 44},
      ISSN = {1286-4889},
   MRCLASS = {20M30 (05E10)},
  MRNUMBER = {2800981},
MRREVIEWER = {Thomas Pietraho},
}

@article {Norton.1979,
    AUTHOR = {Norton, P. N.},
     TITLE = {{$0$}-{H}ecke algebras},
   JOURNAL = {J. Austral. Math. Soc. Ser. A},
  FJOURNAL = {Australian Mathematical Society. Journal. Series A},
    VOLUME = {27},
      YEAR = {1979},
    NUMBER = {3},
     PAGES = {337--357},
      ISSN = {0263-6115},
   MRCLASS = {16A48 (17B10)},
  MRNUMBER = {532754},
MRREVIEWER = {S. B. Conlon},
}

@article {Carter.1986,
    AUTHOR = {Carter, R. W.},
     TITLE = {Representation theory of the {$0$}-{H}ecke algebra},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {104},
      YEAR = {1986},
    NUMBER = {1},
     PAGES = {89--103},
      ISSN = {0021-8693},
   MRCLASS = {20C15 (16A65 20G05)},
  MRNUMBER = {865891},
MRREVIEWER = {David Benson},
       URL = {https://doi.org/10.1016/0021-8693(86)90238-3},
}
@book {Pin.2010, 
    AUTHOR = {Jean-Eric Pin},
    TITLE = {Mathematical Foundations of Automata Theory},
    YEAR = {2010},
    URL = {http://www.liafa.jussieu.fr/~jep/MPRI/MPRI.html},
}

@article {GanMaz.2006,
    AUTHOR = {Ganyushkin, Olexandr and Mazorchuk, Volodymyr},
     TITLE = {Combinatorics and distributions of partial injections},
   JOURNAL = {Australasian J. of Comb.},
  FJOURNAL = {Australasian Journal of Combinatorics},
    VOLUME = {34},
      YEAR = {2006},
     PAGES = {161--186},
      ISSN = {2202-3518}
}


@article {Fayers.2005,
    AUTHOR = {Fayers, Matthew},
     TITLE = {0-{H}ecke algebras of finite {C}oxeter groups},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {199},
      YEAR = {2005},
    NUMBER = {1-3},
     PAGES = {27--41},
      ISSN = {0022-4049},
   MRCLASS = {20C08},
  MRNUMBER = {2134290},
MRREVIEWER = {Robert B\'edard},
       URL = {https://doi.org/10.1016/j.jpaa.2004.12.001},
}


@article {BergeronLi.2009,
    AUTHOR = {Bergeron, Nantel and Li, Huilan},
     TITLE = {Algebraic structures on {G}rothendieck groups of a tower of
              algebras},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {321},
      YEAR = {2009},
    NUMBER = {8},
     PAGES = {2068--2084},
      ISSN = {0021-8693},
   MRCLASS = {16T30 (05E05 05E15)},
  MRNUMBER = {2501510},
MRREVIEWER = {Mark J. Wildon},
       URL = {https://doi.org/10.1016/j.jalgebra.2008.12.005},
}

@article {Virmaux.2014,
    AUTHOR = {Aladin Virmaux},
    TITLE = {Partial categorification of Hopf algebras and representation theory of towers of $\mathcal{J}$-trivial monoids},
    JOURNAL = {Proceeding of FPSAC 2014 in DMTCS proc. AT},
    YEAR = {2014},
    PAGES = {741-752},
}

@article {KrobThibon.1997,
    AUTHOR = {Krob, Daniel and Thibon, Jean-Yves},
     TITLE = {Noncommutative symmetric functions. {IV}. {Q}uantum linear
              groups and {H}ecke algebras at {$q=0$}},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {6},
      YEAR = {1997},
    NUMBER = {4},
     PAGES = {339--376},
      ISSN = {0925-9899},
   MRCLASS = {05E05 (17B37 20C30)},
  MRNUMBER = {1471894},
MRREVIEWER = {Jian-yi Shi},
       URL = {https://doi.org/10.1023/A:1008673127310},
}

@ARTICLE{Thibon.1998,
    author = {Jean-yves Thibon},
    title = {Lectures On Noncommutative Symmetric Functions},
    journal = {39–94, Math. Soc. Japan Memoirs},
    year = {1998},
    volume = {11},
    pages = {39--94}
}

@Book{MacDonald.1995,
  author	= {Macdonald, I. G.},
  title		= {Symmetric functions and {H}all polynomials},
  series	= {Oxford Mathematical Monographs},
  edition	= {Second},
  note		= {With contributions by A. Zelevinsky, Oxford Science
		  Publications},
  publisher	= {The Clarendon Press Oxford University Press},
  address	= {New York},
  year		= {1995},
  pages		= {x+475},
  isbn		= {0-19-853489-2},
  mrclass	= {05E05 (05-02 20C30 20C33 20K01 33C80 33D80)},
  mrnumber	= {MR1354144 (96h:05207)},
  mrreviewer	= {John R. Stembridge}
}

@InCollection{Gessel.1984,
  author	= {Gessel, Ira M.},
  title		= {Multipartite {$P$}-partitions and inner products of skew
		  {S}chur functions},
  booktitle	= {Combinatorics and algebra (Boulder, Colo., 1983)},
  series	= {Contemp. Math.},
  volume	= {34},
  pages		= {289--317},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1984},
  mrclass	= {05A17 (20C30)},
  mrnumber	= {MR777705 (86k:05007)},
  mrreviewer	= {J. D{\'e}sarm{\'e}nien}
}

@book{Lothaire.2002,
place={Cambridge},
series={Encyclopedia of Mathematics and its Applications},
title={Algebraic Combinatorics on Words},
DOI={10.1017/CBO9781107326019},
publisher={Cambridge University Press},
author={Lothaire, M.},
year={2002},
collection={Encyclopedia of Mathematics and its Applications}}

@Article{	  Denton.2010,
  title		= {{A combinatorial formula for orthogonal idempotents in the
		  $0$-{H}ecke algebra of the symmetric group}},
  author	= {Denton, Tom},
  year		= {2010},
  note		= {preprint arXiv:1008.2401v1 [math.RT]}
}

@Article{	  Miller.2005,
  author	= {Miller, Ezra},
  title		= {Alternating formulas for {$K$}-theoretic quiver
		  polynomials},
  journal	= {Duke Math. J.},
  fjournal	= {Duke Mathematical Journal},
  volume	= {128},
  year		= {2005},
  number	= {1},
  pages		= {1--17},
  issn		= {0012-7094},
  coden		= {DUMJAO},
  mrclass	= {05E05 (14C17)},
  mrnumber	= {2137947 (2006e:05181)},
  mrreviewer	= {Harry Tamvakis},
  doi		= {10.1215/S0012-7094-04-12811-8},
}

@Article{	  Lam_Schilling_Shimozono.2010,
  author	= {Lam, Thomas and Schilling, Anne and Shimozono, Mark},
  title		= {{$K$}-theory {S}chubert calculus of the affine
		  {G}rassmannian},
  journal	= {Compos. Math.},
  fjournal	= {Compositio Mathematica},
  volume	= {146},
  year		= {2010},
  number	= {4},
  pages		= {811--852},
  issn		= {0010-437X},
  mrclass	= {14N15 (05E05)},
  mrnumber	= {2660675},
  doi		= {10.1112/S0010437X09004539},
}

@Misc{sage-semigroup,
author =   {Hivert, Florent and Saliola, Franco and
Thiéry, Nicolas~M. et al.},
title =    {{sage-semigroup}: A semigroup (representation) theory library for
                  SageMath},
howpublished = {\url{https://github.com/nthiery/sage-semigroups/}},
year = {2012--2018},
}

@Misc{libsemigroup,
author =   {Mitchell, James d. and Torpey, Michael},
title =    {{L}ib{S}emigroup: A library for semigroups and monoids - Version
                  0.6.3 },
howpublished = {\url{https://james-d-mitchell.github.io/libsemigroups/}},
year = {2018},
}

@Manual{          Sagemath,
  key           = {SAGE},
  author        = {W.\thinspace{}A. Stein and others},
  organization  = {The Sage~Development Team},
  title         = {{S}age {M}athematics {S}oftware},
  url           = {http://www.sagemath.org},
  year          = 2018
}


@book{riordan2002introduction,
  title={Introduction to Combinatorial Analysis},
  author={Riordan, J.},
  isbn={9780486425368},
  lccn={2002073535},
  series={Dover Books on Mathematics},
  url={https://books.google.fr/books?id=zWgIPlds29UC},
  year={2002},
  publisher={Dover Publications}
}

@article{JosuatVerges.2011,
title = "Rook placements in Young diagrams and permutation enumeration",
journal = "Advances in Applied Mathematics",
volume = "47",
number = "1",
pages = "1 - 22",
year = "2011",
issn = "0196-8858",
doi = "https://doi.org/10.1016/j.aam.2010.04.003",
url = "http://www.sciencedirect.com/science/article/pii/S0196885810000515",
author = "Matthieu Josuat-Vergès",
keywords = "PASEP, Permutation tableaux, Rook placements, Permutation pattern, Orthogonal polynomials",
abstract = "Given two operators Dˆ and Eˆ subject to the relation DˆEˆ−qEˆDˆ=p, and a word w in Dˆ and Eˆ, the rewriting of w in normal form is combinatorially described by rook placements in Young diagrams. We give enumerative results about these rook placements, particularly in the case where p=(1−q)/q2. This case naturally arises in the context of the PASEP, a random process whose partition function and stationary distribution can be derived using two operators D and E subject to the relation DE−qED=D+E (matrix Ansatz). Using the link obtained by Corteel and Williams between the PASEP, permutation tableaux and permutations, we prove a conjecture of Corteel and Rubey about permutation enumeration. This result gives the generating function for permutations of given size with respect to the number of ascents and occurrences of the pattern 13-2, this is also the moments of some q-Laguerre orthogonal polynomials."
}


@Article{	  GayHivert.2018,
  author	= {Gay, Jo\"{e}l and Hivert, Florent},
  title		= {The {$0$}-{R}enner monoids},
  year    = {2018},
  archivePrefix = {arXiv},
  eprint = {fixme},
  primaryClass = {math-co},
  VOLUME  = {},
   NUMBER  = {},
   PAGES   = {60}
}

@MISC{Butler_rooktheory,
    author = {Butler, Fred and Haglund, Jim and Can, Mahir and Remmel, Jeffrey B.},
    title = {Rook Theory Notes},
    year = 2010
}

@article{MannevillePilaud.2017,
title = "Compatibility fans for graphical nested complexes",
journal = "Journal of Combinatorial Theory, Series A",
volume = "150",
pages = "36 - 107",
year = "2017",
issn = "0097-3165",
doi = "https://doi.org/10.1016/j.jcta.2017.02.004",
url = "http://www.sciencedirect.com/science/article/pii/S009731651730016X",
author = "Thibault Manneville and Vincent Pilaud",
keywords = "Graph associahedra, Finite type cluster algebras, Compatibility degrees, Compatibility fans",
abstract = "Graph associahedra generalize classical associahedra. They realize the nested complex of a graph G, i.e. the simplicial complex whose vertices are the tubes (connected induced subgraphs) of G and whose faces are the tubings (collections of pairwise nested or non-adjacent tubes) of G. The constructions of M. Carr and S. Devadoss, of A. Postnikov, and of A. Zelevinsky for graph associahedra are all based on the nested fan, which coarsens the normal fan of the permutahedron. In view of the variety of fan realizations of associahedra, it is tempting to look for alternative fans realizing graphical nested complexes. Motivated by the analogy between finite type cluster complexes and graphical nested complexes, we transpose S. Fomin and A. Zelevinsky's compatibility fans from the former to the latter setting. We define a compatibility degree between two tubes of a graph G and show that the compatibility vectors of all tubes of G with respect to an arbitrary maximal tubing on G support a fan realizing the nested complex of G. When G is a path, we recover F. Santos' Catalan many realizations of the associahedron."
}

@book {ZieglerGeom,
    AUTHOR = {Ziegler, G\"unter M.},
     TITLE = {Lectures on polytopes},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {152},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {1995},
     PAGES = {x+370},
      ISBN = {0-387-94365-X},
   MRCLASS = {52Bxx},
  MRNUMBER = {1311028},
MRREVIEWER = {Margaret M. Bayer},
       URL = {https://doi.org/10.1007/978-1-4613-8431-1},
}



@article {GuilbaudRosenstiehl,
    AUTHOR = {Guilbaud, Georges Th. and Rosenstiehl, Pierre},
     TITLE = {Analyse algébrique d'un scrutin},
   JOURNAL = {Math. Sci. Hum.},
  FJOURNAL = {Mathématiques et Sciences Humaines},
    VOLUME = {4},
      YEAR = {1963},
     PAGES = {9-33},
}



@article {HohlwegLange.2007,
    AUTHOR = {Hohlweg, Christophe and Lange, Carsten E. M. C.},
     TITLE = {Realizations of the associahedron and cyclohedron},
   JOURNAL = {Discrete Comput. Geom.},
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}


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@misc{LabbeLange.2018,
Author = {Jean-Philippe Labbé and Carsten Lange},
Title = {Cambrian acyclic domains: counting $c$-singletons},
Year = {2018},
Eprint = {arXiv:1802.07978},
}


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@article {ViennotHeap,
author="Viennot, G{\'e}rard Xavier",
editor="Labelle, Gilbert
and Leroux, Pierre",
title="Heaps of pieces, I : Basic definitions and combinatorial lemmas",
booktitle="Combinatoire {\'e}num{\'e}rative",
year="1986",
journal="Lecture Notes in Mathematics",
volume="1234",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="321--350",
abstract="We introduce the combinatorial notion of heaps of pieces, which gives a geometric interpretation of the Cartier-Foata's commutation monoid. This theory unifies and simplifies many other works in Combinatorics : bijective proofs in matrix algebra (MacMahon Master theorem, inversion matrix formula, Jacobi identity, Cayley-Hamilton theorem), combinatorial theory for general (formal) orthogonal polynomials, reciprocal of Rogers-Ramanujan identities, graph theory (matching and chromatic polynomials). Heaps may bring new light on classical subjects as poset theory. They are related to other fields as Theoretical Computer Science (parallelism) and Statistical Physics (directed animals problem, lattice gas model with hard-core interactions). Complete proofs and definitions are given in sections 2, 3,4,5. Other sections give a summary of possible applications of heaps.",
isbn="978-3-540-47402-9"
}



@misc{ViennotWeb,
author="Viennot, G{\'e}rard Xavier",
Title = {Course {IMS}c {C}hennai, {I}ndia},
Year = {2017},
volume={Chapter 6a},
url = {http://coursimsc2017.xavierviennot.org/}
}

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  author = {Sergey Fomin},
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}

@article{Fomin1995,
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  year = {1995},
  publisher = {Springer Science and Business Media {LLC}},
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  author = {Sergey Fomin},
  journal = {Journal of Algebraic Combinatorics}
}

@article{Killpatrick2005,
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@phdthesis{Roby1991,
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  school={Massachusetts Institute of Technology}
}

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@book {Mathas1999,
    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, Providence, RI},
      YEAR = {1999},
     PAGES = {xiv+188},
      ISBN = {0-8218-1926-7},
   MRCLASS = {20C08 (20C20 20G99)},
  MRNUMBER = {1711316},
MRREVIEWER = {Meinolf\ Geck},
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       URL = {https://doi.org/10.1090/ulect/015},
}

@article{Martin1994a,
  abstract = {We determine the structure of two variations on the Temperley-Lieb algebra, both used for dealing with special kinds of boundary conditions in statistical mechanics models. The first is a new algebra, the "blob" algebra. We determine both the generic and all the exceptional structures for this two parameter algebra. The second is the periodic Temperley-Lieb algebra. The generic structure and part of the exceptional structure of this algebra have already been studied. We complete the analysis using results from the study of the blob algebra.},
  added-at = {2009-05-07T15:23:46.000+0200},
  author = {Martin, Paul and Saleur, Hubert},
  biburl = {https://www.bibsonomy.org/bibtex/2c1f957435f722c0e30751ae783b41e66/njj},
  coden = {LMPHDY},
  doi = {10.1007/BF00805852},
  fjournal = {Letters in Mathematical Physics},
  interhash = {697cc946c9590f4c2d65a493285ac581},
  intrahash = {c1f957435f722c0e30751ae783b41e66},
  issn = {0377-9017},
  journal = {Lett. Math. Phys.},
  keywords = {algebra representation-theory temperley-lieb},
  mrclass = {81R50 (16S99 82B23)},
  mrkey = {1267001},
  mrreviewer = {Andrey V. Tsiganov},
  number = 3,
  pages = {189--206},
  timestamp = {2009-05-07T15:23:46.000+0200},
  title = {The blob algebra and the periodic Temperley-Lieb algebra},
  url = {http://www.springerlink.com/content/r6n8337025v53876/?p=6a34558dc095429c9f97a0a0c7d1ff4c&pi=3},
  volume = 30,
  year = 1994
}

@article{Graham1996CellularA,
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  url={https://api.semanticscholar.org/CorpusID:189831103}
}