@article {Anderson.Griffeth.Miller, AUTHOR = {Anderson, D. and Griffeth, S. and Miller, E.}, TITLE = {Positivity and {K}leiman transversality in equivariant {$K$}-theory of homogeneous spaces}, JOURNAL = {J. Eur. Math. Soc. (JEMS)}, FJOURNAL = {Journal of the European Mathematical Society (JEMS)}, VOLUME = {13}, YEAR = {2011}, NUMBER = {1}, PAGES = {57--84}, } @article {Assaf.Searles, author = {Assaf, Sami and Searles, Dominic}, title = {Schubert polynomials, slide polynomials, {S}tanley symmetric functions and quasi-{Y}amanouchi pipe dreams}, journal = {Adv. Math.}, year = {2017}, volume={306}, pages = {89--122}, } @book {Baxter, AUTHOR = {Baxter, R. J.}, TITLE = {Exactly solved models in statistical mechanics}, PUBLISHER = {Academic Press, Inc., London}, YEAR = {1982}, PAGES = {xii+486}, } @article {Berg.Bergeron.Saliola.Serrano.Zabrocki, AUTHOR = {Berg, Chris and Bergeron, Nantel and Saliola, Franco and Serrano, Luis and Zabrocki, Mike}, TITLE = {Indecomposable modules for the dual immaculate basis of quasi-symmetric functions}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {143}, YEAR = {2015}, NUMBER = {3}, PAGES = {991--1000}, } @article {Bergeron.Billey, AUTHOR = {Bergeron, N. and Billey, S.}, TITLE = {R{C}-graphs and {S}chubert polynomials}, JOURNAL = {Experiment. Math.}, FJOURNAL = {Experimental Mathematics}, VOLUME = {2}, YEAR = {1993}, NUMBER = {4}, PAGES = {257--269}, } @article {Bernstein.Gelfand.Gelfand, AUTHOR = {Bern\v{s}te\u{\i}n, I. N. and Gel'fand, I. M. and Gel'fand, S. I.}, TITLE = {Schubert cells, and the cohomology of the spaces {$G/P$}}, JOURNAL = {Uspehi Mat. Nauk}, FJOURNAL = {Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk}, VOLUME = {28}, YEAR = {1973}, NUMBER = {3(171)}, PAGES = {3--26}, } @article {Billey.Jockusch.Stanley, AUTHOR = {Billey, Sara C. and Jockusch, William and Stanley, Richard P.}, TITLE = {Some combinatorial properties of {S}chubert polynomials}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {2}, YEAR = {1993}, NUMBER = {4}, PAGES = {345--374}, } @article{Billey.Holroyd.Young, title={A bijective proof of {M}acdonald's reduced word formula}, author={Billey, Sara C. and Holroyd, Alexander E. and Young, Benjamin}, journal={Algebraic Combin.}, note={to appear, {\sf arXiv:1702.02936}}, year={2018}, pages = {39 pages}, } @article {Bloom.Pechenik.Saracino, AUTHOR = {Bloom, Jonathan and Pechenik, Oliver and Saracino, Dan}, TITLE = {Proofs and generalizations of a homomesy conjecture of {P}ropp and {R}oby}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {339}, YEAR = {2016}, NUMBER = {1}, PAGES = {194--206}, } @article {Borel, AUTHOR = {Borel, A.}, TITLE = {Sur la cohomologie des espaces fibr\'{e}s principaux et des espaces homog\`enes de groupes de {L}ie compacts}, JOURNAL = {Ann. of Math.}, VOLUME = {57}, YEAR = {1953}, PAGES = {115--207}, } @article {Bressler.Evens, AUTHOR = {Bressler, Paul and Evens, Sam}, TITLE = {The {S}chubert calculus, braid relations, and generalized cohomology}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {317}, YEAR = {1990}, NUMBER = {2}, PAGES = {799--811}, } @book {Bressoud, AUTHOR = {Bressoud, D.}, TITLE = {Proofs and confirmations: the story of the alternating sign matrix conjecture}, SERIES = {MAA Spectrum}, PUBLISHER = {Mathematical Association of America, Washington, DC; Cambridge University Press, Cambridge}, YEAR = {1999}, PAGES = {xvi+274}, } @article {Brion, AUTHOR = {Brion, Michel}, TITLE = {Positivity in the {G}rothendieck group of complex flag varieties}, NOTE = {Special issue in celebration of Claudio Procesi's 60th birthday}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {258}, YEAR = {2002}, NUMBER = {1}, PAGES = {137--159}, } @incollection {Bruns.Conca, AUTHOR = {Bruns, W. and Conca, A.}, TITLE = {Gr\"{o}bner bases and determinantal ideals}, BOOKTITLE = {Commutative algebra, singularities and computer algebra ({S}inaia, 2002)}, SERIES = {NATO Sci. Ser. II Math. Phys. Chem.}, VOLUME = {115}, PAGES = {9--66}, PUBLISHER = {Kluwer Acad. Publ., Dordrecht}, YEAR = {2003}, } @article {Buch, AUTHOR = {Buch, Anders Skovsted}, TITLE = {A {L}ittlewood-{R}ichardson rule for the {$K$}-theory of {G}rassmannians}, JOURNAL = {Acta Math.}, FJOURNAL = {Acta Mathematica}, VOLUME = {189}, YEAR = {2002}, NUMBER = {1}, PAGES = {37--78}, } @article {Buch.Ravikumar, AUTHOR = {Buch, Anders Skovsted and Ravikumar, Vijay}, TITLE = {Pieri rules for the {$K$}-theory of cominuscule {G}rassmannians}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's Journal]}, VOLUME = {668}, YEAR = {2012}, PAGES = {109--132}, } @article {Buch.Samuel, author = {Buch, Anders Skovsted and Samuel, Matthew J.}, title = {${K}$-theory of minuscule varieties}, journal = {J. Reine Angew. Math.}, volume = {719}, year = {2016}, pages = {133--171} } @article{Conca.DeNegri.Gorla, author = {Conca, A. and De Negri, E. and Gorla, E.}, title = "{Universal {G}r\"{o}bner bases for maximal minors}", JOURNAL = {Int. Math. Res. Not. IMRN}, volume = {2015}, number = {11}, pages = {3245-3262}, year = {2015}, } @article {Clifford.Thomas.Yong, AUTHOR = {Clifford, Edward and Thomas, Hugh and Yong, Alexander}, TITLE = {{$K$}-theoretic {S}chubert calculus for {${\rm OG}(n,2n+1)$} and jeu de taquin for shifted increasing tableaux}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's Journal]}, VOLUME = {690}, YEAR = {2014}, PAGES = {51--63}, } @incollection {Coskun.Vakil, AUTHOR = {Co\c{s}kun, I. and Vakil, R.}, TITLE = {Geometric positivity in the cohomology of homogeneous spaces and generalized {S}chubert calculus}, BOOKTITLE = {Algebraic geometry---{S}eattle 2005. {P}art 1}, SERIES = {Proc. Sympos. Pure Math.}, VOLUME = {80}, PAGES = {77--124}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {2009}, } @book {Cox.Little.OShea, AUTHOR = {Cox, David and Little, John and O'Shea, Donal}, TITLE = {Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra}, SERIES = {Undergraduate Texts in Mathematics}, EDITION = {3rd}, PUBLISHER = {Springer, New York}, YEAR = {2007}, PAGES = {xvi+551}, ISBN = {978-0-387-35650-1; 0-387-35650-9}, } @article {DPS, author = {Dilks, Kevin and Pechenik, Oliver and Striker, Jessica}, title = {Resonance in orbits of plane partitions and increasing tableaux}, journal = {J. Combin. Theory Ser. A}, year ={2017}, volume = {148}, pages = {244--274} } @article {Dong.Wang, author = {Dong, Chao-Ping and Wang, Suijie}, title = {Homomesy in the graded poset $\triangle(1)$}, journal = {preprint}, year = {2016}, note = {{\sf arXiv:1606.05715}} } @article {Duchamp.Krob.Leclerc.Thibon, AUTHOR = {Duchamp, G\'{e}rard and Krob, Daniel and Leclerc, Bernard and Thibon, Jean-Yves}, TITLE = {Fonctions quasi-sym\'{e}triques, fonctions sym\'{e}triques non commutatives et alg\`ebres de {H}ecke \`a {$q=0$}}, JOURNAL = {C. R. Acad. Sci. Paris S\'{e}r. I Math.}, FJOURNAL = {Comptes Rendus de l'Acad\'{e}mie des Sciences. S\'{e}rie I. Math\'{e}matique}, VOLUME = {322}, YEAR = {1996}, NUMBER = {2}, PAGES = {107--112}, } @article {Edelman.Greene, AUTHOR = {Edelman, Paul and Greene, Curtis}, TITLE = {Balanced tableaux}, JOURNAL = {Adv. in Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {63}, YEAR = {1987}, NUMBER = {1}, PAGES = {42--99}, } @article {Egecioglu.Remmel, AUTHOR = {E\u{g}ecio\u{g}lu, \"Omer and Remmel, Jeffrey B.}, TITLE = {A combinatorial interpretation of the inverse {K}ostka matrix}, JOURNAL = {Linear and Multilinear Algebra}, FJOURNAL = {Linear and Multilinear Algebra}, VOLUME = {26}, YEAR = {1990}, NUMBER = {1-2}, PAGES = {59--84}, } @article {Egge.Loehr.Warrington, AUTHOR = {Egge, Eric and Loehr, Nicholas A. and Warrington, Gregory S.}, TITLE = {From quasisymmetric expansions to {S}chur expansions via a modified inverse {K}ostka matrix}, JOURNAL = {European J. Combin.}, FJOURNAL = {European Journal of Combinatorics}, VOLUME = {31}, YEAR = {2010}, NUMBER = {8}, PAGES = {2014--2027}, } @article {Eilenberg.MacLane, AUTHOR = {Eilenberg, Samuel and Mac Lane, Saunders}, TITLE = {On the groups of {$H(\Pi,n)$}. {I}}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {58}, YEAR = {1953}, PAGES = {55--106}, } @article {EFGJMPR, author = {Einstein, David and Farber, Miriam and Gunawan, Emily and Joseph, Michael and Macauley, Matthew and Propp, James and Rubinstein-Salzedo, Simon}, title = {Noncrossing partitions, toggles, and homomesies}, journal = {Electron. J. Combin.}, year = {2016}, volume = {23}, pages = {1--26}, } @incollection {Einstein.Propp, AUTHOR = {Einstein, David and Propp, James}, TITLE = {Piecewise-linear and birational toggling}, BOOKTITLE = {26th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2014)}, SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AT}, PAGES = {513--524}, PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy}, YEAR = {2014}, } @article {Elkies.Kuperberg.Larsen.Propp, AUTHOR = {Elkies, N. and Kuperberg, G. and Larsen, M. and Propp, J.}, TITLE = {Alternating-sign matrices and domino tilings. {II}}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {1}, YEAR = {1992}, NUMBER = {3}, PAGES = {219--234}, } @article {Fink.Meszaros.StDizier, author = {Fink, A. and M\'{e}sz\'{a}ros, K. and St. Dizier, A.}, title = {Zero-one {S}chubert polynomials}, journal = {preprint}, year = {2019}, note = {{\sf arXiv:1903.10332}}, pages = {16 pages}, } @incollection {Fomin.Kirillov, AUTHOR = {Fomin, S. and Kirillov, A. N.}, TITLE = {Grothendieck polynomials and the {Y}ang-{B}axter equation}, BOOKTITLE = {Formal power series and algebraic combinatorics/{S}\'eries formelles et combinatoire alg\'ebrique}, PAGES = {183--189}, PUBLISHER = {DIMACS, Piscataway, NJ}, YEAR = {1994}, } @article {Fomin.Stanley, AUTHOR = {Fomin, Sergey and Stanley, Richard P.}, TITLE = {Schubert polynomials and the nil-{C}oxeter algebra}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {103}, YEAR = {1994}, NUMBER = {2}, PAGES = {196--207}, } @article {Fulton, AUTHOR = {Fulton, W.}, TITLE = {Flags, {S}chubert polynomials, degeneracy loci, and determinantal formulas}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {65}, YEAR = {1992}, NUMBER = {3}, PAGES = {381--420}, } @article {Fulton.Lascoux, AUTHOR = {Fulton, W. and Lascoux, A.}, TITLE = {A {P}ieri formula in the {G}rothendieck ring of a flag bundle}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {76}, YEAR = {1994}, NUMBER = {3}, PAGES = {711--729}, } @book {Fulton.Pragacz, AUTHOR = {Fulton, W. and Pragacz, P.}, TITLE = {Schubert varieties and degeneracy loci}, SERIES = {Lecture Notes in Mathematics}, VOLUME = {1689}, PUBLISHER = {Springer-Verlag, Berlin}, YEAR = {1998}, PAGES = {xii+148}, } @article {GMPPRST, AUTHOR = {Gaetz, Christian and Mastrianni, Michelle and Patrias, Rebecca and Peck, Hailee and Robichaux, Colleen and Schwein, David and Tam, Ka Yu}, TITLE = {{$K$}-{K}nuth equivalence for increasing tableaux}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {23}, YEAR = {2016}, NUMBER = {1}, PAGES = {Paper 1.40, 37}, } @article {Gaetz.Gao, author = {Gaetz, Christian and Gao, Yibo}, title = {A combinatorial {$\mathfrak{sl}_2$}-action and the {S}perner property for the weak order}, journal = {preprint}, year = {2018}, note = {{\sf arXiv:1811.05501}}, pages = {6 pages}, } @article {Gaetz.Gao:2, author = {Gaetz, Christian and Gao, Yibo}, title = {A combinatorial duality between the weak and strong {B}ruhat orders}, journal = {preprint}, year = {2018}, note = {{\sf arXiv:1812.05126}}, pages = {14 pages}, } @article {Garsia.Remmel, author = {Garsia, Adriano and Remmel, Jeffrey}, title = {A note on passing from a quasi-symmetric function expansion to a {S}chur function expansion of a symmetric function}, journal = {preprint}, year = {2018}, note = {{\sf arXiv:1802.09686}}, pages = {7 pages}, } @incollection {Gessel, AUTHOR = {Gessel, Ira M.}, TITLE = {Multipartite {$P$}-partitions and inner products of skew {S}chur functions}, BOOKTITLE = {Combinatorics and algebra ({B}oulder, {C}olo., 1983)}, SERIES = {Contemp. Math.}, VOLUME = {34}, PAGES = {289--317}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {1984}, } @article {Gessel:expansion, author = {Gessel, Ira M.}, title = {On the {S}chur function expansion of a symmetric quasi-symmetric function}, journal = {preprint}, year = {2018}, note = {{\sf arXiv:1803.09271}}, pages = {4 pages}, } @article {Gillespie.Levinson, AUTHOR = {Gillespie, Maria Monks and Levinson, Jake}, TITLE = {Monodromy and {K}-theory of {S}chubert curves via generalized jeu de taquin}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {45}, YEAR = {2017}, NUMBER = {1}, PAGES = {191--243}, } @article {Gonciulea.Miller, AUTHOR = {Gonciulea, N. and Miller, C.}, TITLE = {Mixed ladder determinantal varieties}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {231}, YEAR = {2000}, NUMBER = {1}, PAGES = {104--137}, } @article {Haiman, AUTHOR = {Haiman, Mark D.}, TITLE = {Dual equivalence with applications, including a conjecture of {P}roctor}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {99}, YEAR = {1992}, NUMBER = {1-3}, PAGES = {79--113}, } @article {Hamaker.Patrias.Pechenik.Williams, author = {Hamaker, Zachary and Patrias, Rebecca and Pechenik, Oliver and Williams, Nathan}, title = {Doppelg\"{a}ngers: Bijections of plane partitions}, journal = {preprint}, year = {2016}, note = {{\sf arXiv:1602.05535}} } @article {Hamaker.Pechenik.Speyer.Weigandt, author = {Hamaker, Zachary and Pechenik, Oliver and Speyer, David E and Weigandt, Anna}, title = {Derivatives of {S}chubert polynomials and proof of a determinant conjecture of {S}tanley}, journal = {Algebraic Combin., to appear}, year = {2020}, note = {{\sf arXiv:1812.00321}} } @article {Hamaker.Pechenik.Weigandt, author = {Hamaker, Z. and Pechenik, O. and Weigandt, A.}, title = {Gr\"{o}bner geometry of {S}chubert polynomials through ice}, journal = {preprint}, year = {2020}, eprint = {2003.13719}, pages = {22 pages}, } @article {Heck, author = {Heck, R.}, title = {Duplicitous permutations and bumpless pipe dreams}, journal = {preprint}, year = {2019}, url = {https://lsa.umich.edu/content/dam/math-assets/math-document/reu-documents/ugradreu/2019/Heck,Laurel.pdf}, } @article {Hopkins.Zhang, AUTHOR = {Hopkins, Sam and Zhang, Ingrid}, TITLE = {A note on statistical averages for oscillating tableaux}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {22}, YEAR = {2015}, NUMBER = {2}, PAGES = {Paper 2.48, 9}, } @article {Huang, AUTHOR = {Huang, Jia}, TITLE = {A tableau approach to the representation theory of 0-{H}ecke algebras}, JOURNAL = {Ann. Comb.}, FJOURNAL = {Annals of Combinatorics}, VOLUME = {20}, YEAR = {2016}, NUMBER = {4}, PAGES = {831--868}, ISSN = {0218-0006}, } @article {Hudson, AUTHOR = {Hudson, Thomas}, TITLE = {A {T}hom-{P}orteous formula for connective {$K$}-theory using algebraic cobordism}, JOURNAL = {J. K-Theory}, FJOURNAL = {Journal of K-Theory. K-Theory and its Applications in Algebra, Geometry, Analysis \& Topology}, VOLUME = {14}, YEAR = {2014}, NUMBER = {2}, PAGES = {343--369}, } @article{Jockusch.Propp.Shor, author = {Jockusch, William and Propp, James and Shor, Peter}, title = {Random domino tilings and the arctic circle theorem}, journal = {preprint}, year ={1998}, note = {{\sf arXiv:math/9801068}}, pages = {46 pages}, } @Article{Joseph.Roby, author = {Joseph, Michael and Roby, Tom}, title = {Toggling independent sets of a path graph}, journal = {preprint}, year = {2017}, note = {{\sf arXiv:1701.04956}}, } @article {Klein, author = {Klein, P.}, title = {Diagonal degenerations of matrix {S}chubert varieties}, journal = {preprint}, year = {2020}, eprint = {2008.01717}, pages = {18 pages}, } @article {Knutson:cotransition, author = {Knutson, A.}, title = {Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula}, journal = {preprint}, year = {2019}, eprint = {1909.13777}, pages = {15 pages}, } @article {Knutson.Miller, AUTHOR = {Knutson, A. and Miller, E.}, TITLE = {Gr\"obner geometry of {S}chubert polynomials}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {161}, YEAR = {2005}, NUMBER = {3}, PAGES = {1245--1318}, } @article {Knutson.Miller.Yong, AUTHOR = {Knutson, A. and Miller, E. and Yong, A.}, TITLE = {Gr\"obner geometry of vertex decompositions and of flagged tableaux}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's Journal]}, VOLUME = {630}, YEAR = {2009}, PAGES = {1--31}, } @article{Knutson.Yong, title={A formula for {K}-theory truncation {S}chubert calculus}, author={Knutson, Allen and Yong, Alexander}, journal={Int. Math. Res. Not.}, volume={2004}, number={70}, pages={3741--3756}, year={2004}, publisher={OUP} } @article{KohnertVeigneau, title={Using {S}chubert basis to compute with multivariate polynomials}, author={Kohnert, A. and Veigneau, S.}, journal={Adv. in Appl. Math.}, volume={19}, number={1}, pages={45--60}, year={1997}, publisher={Academic Press} } @article{Kreiman, title={Schubert classes in the equivariant {K}-theory and equivariant cohomology of the {G}rassmannian}, author={Kreiman, Victor}, journal={preprint}, note={{\sf arXiv:math/0512204}}, year={2005}, pages={27 pages} } @article {Krob.Thibon, 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}, } @article {Kuperberg, AUTHOR = {Kuperberg, G.}, TITLE = {Another proof of the alternating-sign matrix conjecture}, JOURNAL = {Int. Math. Res. Not.}, FJOURNAL = {International Mathematics Research Notices}, YEAR = {1996}, NUMBER = {3}, PAGES = {139--150}, } @article{ Lam.Lee.Shimozono, title={Back stable {S}chubert calculus}, volume={157}, doi={10.1112/S0010437X21007028}, number={5}, journal={Compositio Mathematica}, publisher={London Mathematical Society}, author={Lam, Thomas and Lee, Seung Jin and Shimozono, Mark}, year={2021}, pages={883–962} } @article {Lam.Pylyavskyy, AUTHOR = {Lam, Thomas and Pylyavskyy, Pavlo}, TITLE = {Combinatorial {H}opf algebras and {$K$}-homology of {G}rassmannians}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2007}, NUMBER = {24}, PAGES = {Art. ID rnm125, 48}, } @article {Lascoux:ice, author = {Lascoux, A.}, title = {{C}hern and {Y}ang through ice}, journal = {preprint}, year = {2002}, url = {https://www.math.uwaterloo.ca/~opecheni/lascoux-ice.pdf}, } @article {Lascoux.Schutzenberger, AUTHOR = {Lascoux, A. and Sch{\"u}tzenberger, M.-P.}, TITLE = {Structure de {H}opf de l'anneau de cohomologie et de l'anneau de {G}rothendieck d'une vari\'et\'e de drapeaux}, JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.}, FJOURNAL = {Comptes Rendus des S\'eances de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, VOLUME = {295}, YEAR = {1982}, NUMBER = {11}, PAGES = {629--633}, } @article {Lascoux.Schutzenberger:polynomes, AUTHOR = {Lascoux, A. and Sch\"{u}tzenberger, M.-P.}, TITLE = {Polyn\^{o}mes de {S}chubert}, JOURNAL = {C. R. Acad. Sci. Paris S\'{e}r. I Math.}, FJOURNAL = {Comptes Rendus des S\'{e}ances de l'Acad\'{e}mie des Sciences. S\'{e}rie I. Math\'{e}matique}, VOLUME = {294}, YEAR = {1982}, NUMBER = {13}, PAGES = {447--450}, } @article {Lascoux.Schutzenberger:tree, AUTHOR = {Lascoux, A. and Sch\"{u}tzenberger, M.-P.}, TITLE = {Schubert polynomials and the {L}ittlewood-{R}ichard-son rule}, 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 = {2-3}, PAGES = {111--124}, } @article {Lenart, AUTHOR = {Lenart, Cristian}, TITLE = {A unified approach to combinatorial formulas for {S}chubert polynomials}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {20}, YEAR = {2004}, NUMBER = {3}, PAGES = {263--299}, } @Article{Lesieur, author = {L. Lesieur}, title = {Les problemes d'intersection sur une vari\'{e}t\'{e} de {G}rassmann}, journal = {C. R. Acad. Sci. Paris}, year = {1947}, volume = {225}, pages = {916--917}, } @article {Littlewood.Richardson, author = {Littlewood, D. E. and Richardson, A. R.}, title = {Group Characters and Algebra}, volume = {233}, number = {721-730}, pages = {99--141}, year = {1934}, publisher = {The Royal Society}, fjournal = {Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences}, journal = {Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.} } @book {Macdonald, AUTHOR = {Macdonald, I. G.}, TITLE = {Symmetric functions and {H}all polynomials}, SERIES = {Oxford Classic Texts in the Physical Sciences}, EDITION = {Second edition}, NOTE = {With contribution by A. V. Zelevinsky and a foreword by Richard Stanley, Reprint of the 2008 paperback edition}, PUBLISHER = {The Clarendon Press, Oxford University Press, New York}, YEAR = {2015}, PAGES = {xii+475}, ISBN = {978-0-19-873912-8}, } @Book{Macdonald:notes, author = {I. G. Macdonald}, title = {Notes on {S}chubert polynomials}, publisher = {Publications du LACIM, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al}, year = {1991}, OPTkey = {•}, volume = {6}, } @incollection {Macpherson, AUTHOR = {MacPherson, R.}, TITLE = {Equivariant invariants and linear geometry}, BOOKTITLE = {Geometric combinatorics}, SERIES = {IAS/Park City Math. Ser.}, VOLUME = {13}, PAGES = {317--388}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {2007}, } @book {Manivel, AUTHOR = {Manivel, Laurent}, TITLE = {Symmetric functions, {S}chubert polynomials and degeneracy loci}, SERIES = {SMF/AMS Texts and Monographs}, VOLUME = {6}, NOTE = {Translated from the 1998 French original by John R. Swallow, Cours Sp\'{e}cialis\'{e}s [Specialized Courses], 3}, PUBLISHER = {American Mathematical Society, Providence, RI; Soci\'{e}t\'{e} Math\'{e}matique de France, Paris}, YEAR = {2001}, PAGES = {viii+167}, } @book{miller2004combinatorial, title={Combinatorial commutative algebra}, author={Miller, E. and Sturmfels, B.}, year={2004}, publisher={Springer Science \& Business Media} } @article {Miller:mitosis, AUTHOR = {Miller, E.}, TITLE = {Mitosis recursion for coefficients of {S}chubert polynomials}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {103}, YEAR = {2003}, NUMBER = {2}, PAGES = {223--235}, } @article {Monical, author = {Monical, Cara}, title = {Set-valued skyline fillings}, journal = {preprint}, year = {2016}, note = {{\sf arXiv:1611.08777}}, pages = {17 pages}, } @article{Morales.Pak.Panova, title={Hook formulas for skew shapes {II}. {C}ombinatorial proofs and enumerative applications}, author={Morales, Alejandro H and Pak, Igor and Panova, Greta}, journal={SIAM J. Discrete Math.}, volume={31}, number={3}, pages={1953--1989}, year={2017}, publisher={SIAM} } @article {Norton, 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}, } @article {Panyushev, AUTHOR = {Panyushev, Dmitri I.}, TITLE = {On orbits of antichains of positive roots}, JOURNAL = {European J. Combin.}, FJOURNAL = {European Journal of Combinatorics}, VOLUME = {30}, YEAR = {2009}, NUMBER = {2}, PAGES = {586--594}, } @article {Patrias, title = {Antipode formulas for some combinatorial {H}opf algebras}, author = {Patrias, Rebecca}, journal = {preprint}, year = {2015}, note = {{\sf arXiv:1501.00710}} } @article {Patrias.Pylyavskyy, AUTHOR = {Patrias, Rebecca and Pylyavskyy, Pavlo}, TITLE = {Combinatorics of {$K$}-theory via a {$K$}-theoretic {P}oirier-{R}eutenauer bialgebra}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {339}, YEAR = {2016}, NUMBER = {3}, PAGES = {1095--1115}, } @article {Pechenik, AUTHOR = {Pechenik, Oliver}, TITLE = {Cyclic sieving of increasing tableaux and small {S}chr\"oder paths}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {125}, YEAR = {2014}, PAGES = {357--378}, } @article {Pechenik.Yong:KT, author = {Pechenik, Oliver and Yong, Alexander}, title = {Equivariant ${K}$-theory of {G}rassmannians}, journal = {Forum Math. Pi}, year = {2017}, volume = {5}, pages = {128 pages} } @article {Pechenik.Yong:KT2, AUTHOR = {Pechenik, Oliver and Yong, Alexander}, TITLE = {Equivariant {$K$}-theory of {G}rassmannians {II}: the {K}nutson-{V}akil conjecture}, JOURNAL = {Compos. Math.}, FJOURNAL = {Compositio Mathematica}, VOLUME = {153}, YEAR = {2017}, NUMBER = {4}, PAGES = {667--677}, } @article {Pechenik.Yong:genomic, author = {Pechenik, Oliver and Yong, Alexander}, title = {Genomic tableaux}, journal = {J. Algebraic Combin.}, VOLUME = {45}, YEAR = {2017}, NUMBER = {3}, PAGES = {649--685}, } @article {Pressey.Stokke.Visentin, AUTHOR = {Pressey, Timothy and Stokke, Anna and Visentin, Terry}, TITLE = {Increasing tableaux, {N}arayana numbers and an instance of the cyclic sieving phenomenon}, JOURNAL = {Ann. Comb.}, FJOURNAL = {Annals of Combinatorics}, VOLUME = {20}, YEAR = {2016}, NUMBER = {3}, PAGES = {609--621}, } @article{Proctor:det, title={Product evaluations of {L}efschetz determinants for {G}rassmannians and of determinants of multinomial coefficients}, author={Proctor, Robert A.}, journal={J. Combin. Theory Ser. A}, volume={54}, number={2}, pages={235--247}, year={1990}, } @article {Propp.Roby, AUTHOR = {Propp, James and Roby, Tom}, TITLE = {Homomesy in products of two chains}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {22}, YEAR = {2015}, NUMBER = {3}, PAGES = {Paper 3.4, 29}, } @misc{Propp.Roby:dartmouth, title = "Combinatorial Actions \& Homomesic Orbit Averages", AUTHOR = {Propp, James and Roby, Tom}, year = "23 May 2013", note = "Talk at Dartmouth College Mathematics Colloquium, slides available at {http://www.math.uconn.edu/$\sim$troby/homomesyActions2013DartmouthColloq.pdf}" } @article {Pylyavskyy.Yang, author = {Pylyavskyy, Pavlo and Yang, Jed}, title = {Puzzles in {$K$}-homology of {G}rassmannians}, journal = {preprint}, year = {2018}, note = {{\sf arXiv:1801.07667}}, pages={18 pages}, } @article {Qiu.Remmel, AUTHOR = {Qiu, Dun and Remmel, Jeffrey}, TITLE = {Schur function expansions and the rational shuffle conjecture}, JOURNAL = {S\'em. Lothar. Combin.}, FJOURNAL = {S\'eminaire Lotharingien de Combinatoire}, VOLUME = {78B}, YEAR = {2017}, PAGES = {Art. 83, 13 pages}, } @article {Rhoades:thesis, 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}, } @article {Rhoades:skein, AUTHOR = {Rhoades, Brendon}, TITLE = {A skein action of the symmetric group on noncrossing partitions}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {45}, YEAR = {2017}, NUMBER = {1}, PAGES = {81--127}, ISSN = {0925-9899}, MRCLASS = {05E15 (20C30)}, DOI = {10.1007/s10801-016-0701-y}, URL = {https://dx.doi.org/10.1007/s10801-016-0701-y}, } @article {Robbins.Rumsey, AUTHOR = {Robbins, D. P. and Rumsey, Jr., H.}, TITLE = {Determinants and alternating sign matrices}, JOURNAL = {Adv. in Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {62}, YEAR = {1986}, NUMBER = {2}, PAGES = {169--184}, } @article {Rush.Wang, author = {Rush, David and Wang, Kelvin}, title = {On Orbits of Order Ideals of Minuscule Posets {II}: Homomesy}, journal = {preprint}, year = {2015}, note = {{\sf arXiv:1509.08047}}, } @article {Schutzenberger, AUTHOR = {Sch{\"u}tzenberger, M. P.}, TITLE = {Promotion des morphismes d'ensembles ordonn\'es}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {2}, YEAR = {1972}, PAGES = {73--94}, } @incollection {Sergel, AUTHOR = {Leven, Emily}, TITLE = {Two special cases of the rational shuffle conjecture}, BOOKTITLE = {26th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2014)}, SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AT}, PAGES = {789--800}, PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy}, YEAR = {2014}, } @book {EC2, AUTHOR = {Stanley, Richard P.}, TITLE = {Enumerative combinatorics. {V}ol. 2}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {62}, NOTE = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {1999}, PAGES = {xii+581}, ISBN = {0-521-56069-1; 0-521-78987-7}, } @Article{Stanley:shen, author = {Stanley, Richard P.}, title = {Some {S}chubert shenanigans}, journal = {preprint}, year = {2017}, note = {{\sf arXiv:1704.00851}}, pages = {8 pages} } @article {Stanley:Weyl, AUTHOR = {Stanley, Richard P.}, TITLE = {Weyl groups, the hard {L}efschetz theorem, and the {S}perner property}, JOURNAL = {SIAM J. Algebraic Discrete Methods}, FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on Algebraic and Discrete Methods}, VOLUME = {1}, YEAR = {1980}, NUMBER = {2}, PAGES = {168--184}, } @article {Striker, AUTHOR = {Striker, Jessica}, TITLE = {The toggle group, homomesy, and the {R}azumov-{S}troganov correspondence}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {22}, YEAR = {2015}, NUMBER = {2}, PAGES = {Paper 2.57, 17}, } @article {Sturmfels, AUTHOR = {Sturmfels, B.}, TITLE = {Gr\"{o}bner bases and {S}tanley decompositions of determinantal rings}, JOURNAL = {Math. Z.}, FJOURNAL = {Mathematische Zeitschrift}, VOLUME = {205}, YEAR = {1990}, NUMBER = {1}, PAGES = {137--144}, } @Misc{Tenner:database, author = {Tenner, B.}, title = {Database of permutation pattern avoidance}, howpublished = {electronic database available at {\tt math.depaul.edu/bridget/patterns.html}}, } @article {Tewari.vanWilligenburg, AUTHOR = {Tewari, Vasu V. and van Willigenburg, Stephanie J.}, TITLE = {Modules of the 0-{H}ecke algebra and quasisymmetric {S}chur functions}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {285}, YEAR = {2015}, PAGES = {1025--1065}, ISSN = {0001-8708}, } @article {Thomas.Yong:K, AUTHOR = {Thomas, Hugh and Yong, Alexander}, TITLE = {A jeu de taquin theory for increasing tableaux, with applications to {$K$}-theoretic {S}chubert calculus}, JOURNAL = {Algebra Number Theory}, FJOURNAL = {Algebra \& Number Theory}, VOLUME = {3}, YEAR = {2009}, NUMBER = {2}, PAGES = {121--148}, } @article {Thomas.Yong:Plancherel, AUTHOR = {Thomas, H. and Yong, A.}, TITLE = {Longest increasing subsequences, {P}lancherel-type measure and the {H}ecke insertion algorithm}, JOURNAL = {Adv. in Appl. Math.}, FJOURNAL = {Advances in Applied Mathematics}, VOLUME = {46}, YEAR = {2011}, NUMBER = {1-4}, PAGES = {610--642}, } @article {Thomas.Yong:HT, AUTHOR = {Thomas, Hugh and Yong, Alexander}, TITLE = {Equivariant {S}chubert calculus and jeu de taquin}, JOURNAL = {Ann. Inst. Fourier (Grenoble)}, FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier}, VOLUME = {68}, YEAR = {2018}, NUMBER = {1}, PAGES = {275--318}, } @article {Wachs, AUTHOR = {Wachs, Michelle L.}, TITLE = {Flagged {S}chur functions, {S}chubert polynomials, and symmetrizing operators}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {40}, YEAR = {1985}, NUMBER = {2}, PAGES = {276--289}, } @article{Weigandt, title = {Bumpless pipe dreams and alternating sign matrices}, journal = {Journal of Combinatorial Theory, Series A}, volume = {182}, pages = {105470}, year = {2021}, author = {Anna Weigandt}, doi = {10.1016/j.jcta.2021.105470} } @article{Weigandt.ASM, title={Prism tableaux for alternating sign matrix varieties}, author={Weigandt, A.}, eprint={1708.07236}, year={2017} } @Article{Wheeler.Zinn-Justin, author = {M. Wheeler and P. Zinn-Justin}, title = {Littlewood-{R}ichardson coefficients for {G}rothendieck polynomials from integrability}, journal = {Preprint}, year = {2016}, note = {{\sf arXiv:1607.02396}}, pages = {33 pages} } @article{marberg2020gr, title={Gr\"obner geometry for skew-symmetric matrix {S}chubert varieties}, author={Marberg, Eric and Pawlowski, Brendan}, journal={Preprint}, eprint= {2010.00653}, year={2020} }