@book {BumpSchilling.2017, AUTHOR = {Bump, D. and Schilling, A.}, TITLE = {Crystal bases, Representations and combinatorics}, doi={10.1142/9876}, PUBLISHER = {World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ}, YEAR = {2017}, PAGES = {xii+279}, } @article {BKSRY.2008, AUTHOR = {Buch, A. and Kresch, A. and Shimozono, M. and Tamvakis, H. and Yong, A.}, TITLE = {Stable {G}rothendieck polynomials and {$K$}-theoretic factor sequences}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {340}, doi={10.1007/s00208-007-0155-6}, YEAR = {2008}, NUMBER = {2}, PAGES = {359--382}, } @article {Buch.2002, AUTHOR = {Buch, A.}, TITLE = {A {L}ittlewood-{R}ichardson rule for the {$K$}-theory of {G}rassmannians}, JOURNAL = {Acta Math.}, FJOURNAL = {Acta Mathematica}, doi={10.1007/BF02392644}, VOLUME = {189}, YEAR = {2002}, NUMBER = {1}, PAGES = {37--78}, } @article {FominGreene.1998, AUTHOR = {Fomin, S. and Greene, C.}, TITLE = {Noncommutative {S}chur functions and their applications}, NOTE = {Selected papers in honor of Adriano Garsia (Taormina, 1994)}, JOURNAL = {Discrete Math.}, doi={10.1016/S0012-365X(98)00140-X}, FJOURNAL = {Discrete Mathematics}, VOLUME = {193}, YEAR = {1998}, NUMBER = {1-3}, PAGES = {179--200}, } @misc {FominKirillov.1994, AUTHOR = {Fomin, S. and Kirillov, A.}, TITLE = {Grothendieck polynomials and the {Y}ang-{B}axter equation}, BOOKTITLE = {Formal power series and algebraic combinatorics/{S}\'{e}ries formelles et combinatoire alg\'{e}brique}, PAGES = {183--189}, PUBLISHER = {DIMACS, Piscataway, NJ}, YEAR = {1994}, } @book {Fulton.1996, AUTHOR = {Fulton, W.}, TITLE = {Young Tableaux:}, NOTE = {With Applications to Representation Theory and Geometry}, PUBLISHER = {Cambridge University Press}, doi={10.1017/CBO9780511626241}, SERIES = {London Mathematical Society Student Texts}, YEAR = {1996}, } @book {Garsia2002, AUTHOR = {Garsia, A.}, TITLE = {The Saga of reduced factorizations of elements of the symmetric group}, SERIES = {Publications du Laboratoire de Combinatoire et d'Informatique Math{\'e}matique}, YEAR = {2002}, PUBLISHER = {Universit{\'e} du Qu{\'e}bec {\`a} Montr{\'e}al} } @article {LascouxSchutzenberger.1982, 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\'{e}t\'{e} de drapeaux}, 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 = {295}, YEAR = {1982}, NUMBER = {11}, PAGES = {629--633}, } @misc {LascouxSchutzenberger.1983, AUTHOR = {Lascoux, A. and Sch\"{u}tzenberger, M.-P.}, TITLE = {Symmetry and flag manifolds}, BOOKTITLE = {Invariant theory ({M}ontecatini, 1982)}, SERIES = {Lecture Notes in Math.}, VOLUME = {996}, PAGES = {118--144}, PUBLISHER = {Springer, Berlin}, YEAR = {1983}, } @article {Lenart.2000, AUTHOR = {Lenart, C.}, TITLE = {Combinatorial aspects of the {$K$}-theory of {G}rassmannians}, JOURNAL = {Ann. Comb.}, FJOURNAL = {Annals of Combinatorics}, VOLUME = {4}, doi={10.1007/PL00001276}, YEAR = {2000}, NUMBER = {1}, PAGES = {67--82}, } @article {Monical.2016, AUTHOR = {Monical, C.}, TITLE = {Set-valued skyline fillings}, JOURNAL = {S\'{e}m. Lothar. Combin.}, FJOURNAL = {S\'{e}minaire Lotharingien de Combinatoire}, VOLUME = {78B}, YEAR = {2017}, PAGES = {Art. 35, 12}, } @article {MorseSchilling.2016, AUTHOR = {Morse, J. and Schilling, A.}, TITLE = {Crystal approach to affine {S}chubert calculus}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2016}, doi={10.1093/imrn/rnv194}, NUMBER = {8}, PAGES = {2239--2294}, } @article {MPS.2018, AUTHOR = {Monical, C. and Pechenik, O. and Scrimshaw, T.}, TITLE = {Crystal structures for symmetric {G}rothendieck polynomials}, eprint={1807.03294}, eprinttype={arxiv}, YEAR = {2018} } @article {PP.2016, AUTHOR = {Patrias, R. and Pylyavskyy, P.}, TITLE = {Combinatorics of {$K$}-theory via a {$K$}-theoretic {P}oirier--{R}eute\-nauer bialgebra}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {339}, doi={10.1016/j.disc.2015.10.044}, YEAR = {2016}, NUMBER = {3}, PAGES = {1095--1115}, } @article {RTY.2018, AUTHOR = {Reiner, V. and Tenner, B. and Yong, A.}, TITLE = {Poset edge densities, nearly reduced words, and barely set-valued tableaux}, JOURNAL = {J. Combin. Theory, Ser. A}, FJOURNAL = {Journal of Combinatorial Theory, Series A}, VOLUME = {158}, YEAR = {2018}, doi={10.1016/j.jcta.2018.03.010}, NUMBER = {}, PAGES = {66--125}, } @article {Stanley.1984, AUTHOR = {Stanley, R.}, TITLE = {On the number of reduced decompositions of elements of {C}oxeter groups}, JOURNAL = {European J. Combin.}, FJOURNAL = {European Journal of Combinatorics}, VOLUME = {5}, YEAR = {1984}, doi={10.1016/S0195-6698(84)80039-6}, NUMBER = {4}, PAGES = {359--372}, } @article {Stembridge.2003, AUTHOR = {Stembridge, J.}, TITLE = {A local characterization of simply-laced crystals}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {355}, doi={10.1090/S0002-9947-03-03042-3}, YEAR = {2003}, NUMBER = {12}, PAGES = {4807--4823}, } @article {LamPylyavskyy.2007, AUTHOR = {Lam, T. and Pylyavskyy, P.}, 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}, doi={10.1093/imrn/rnm125}, NUMBER = {24}, PAGES = {Art. ID rnm125, 48}, } @article {BandlowMorse.2012, AUTHOR = {Bandlow, J. and Morse, J.}, TITLE = {Combinatorial expansions in {$K$}-theoretic bases}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {19}, YEAR = {2012}, NUMBER = {4}, PAGES = {Paper 39, 27}, } @article{MPPS.2019, AUTHOR = {Morse, J. and Pan, J. and Poh, W. and Schilling, A.}, TITLE = {A crystal on decreasing factorizations in the $0$-Hecke monoid}, YEAR = {2020}, journal={Electronic J. Comb.}, volume={27(2)}, number={P2.29}, doi={https://doi.org/10.37236/9168} } @article {Lenart.2004, AUTHOR = {Lenart, C.}, 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}, doi={10.1023/B:JACO.0000048515.00922.47}, PAGES = {263--299}, }