% This is an example bibliography file for FPSAC submissions. @article {MorseSchilling, AUTHOR = {Morse, Jennifer and Schilling, Anne}, TITLE = {Crystal approach to affine {S}chubert calculus}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2016}, NUMBER = {8}, PAGES = {2239--2294}, ISSN = {1073-7928,1687-0247}, MRCLASS = {14M15 (14N35)}, MRNUMBER = {3519114}, MRREVIEWER = {Pierre-Emmanuel\ Chaput}, DOI = {10.1093/imrn/rnv194}, URL = {https://doi.org/10.1093/imrn/rnv194}, } @article {BilleyBergeron, AUTHOR = {Bergeron, Nantel and Billey, Sara}, TITLE = {R{C}-graphs and {S}chubert polynomials}, JOURNAL = {Experiment. Math.}, FJOURNAL = {Experimental Mathematics}, VOLUME = {2}, YEAR = {1993}, NUMBER = {4}, PAGES = {257--269}, ISSN = {1058-6458}, MRCLASS = {05E99 (05E05 14M15 20C30)}, MRNUMBER = {1281474}, MRREVIEWER = {Axel Kohnert}, URL = {http://projecteuclid.org/euclid.em/1048516036}, } @article{assaf_demazure_2018, title = {A {Demazure} crystal construction for {Schubert} polynomials}, volume = {1}, issn = {2589-5486}, url = {https://alco.centre-mersenne.org/item/ALCO_2018__1_2_225_0/}, doi = {10.5802/alco.13}, number = {2}, urldate = {2022-09-14}, journal = {Algebraic Combinatorics}, author = {Assaf, Sami and Schilling, Anne}, year = {2018}, pages = {225--247}, file = {Full Text PDF:/Users/sarahgold/Zotero/storage/8CAXRRRK/Assaf and Schilling - 2018 - A Demazure crystal construction for Schubert polyn.pdf:application/pdf;Snapshot:/Users/sarahgold/Zotero/storage/LM4DPQXU/ALCO_2018__1_2_225_0.html:text/html}, } @article{lenart_unified_2004, title = {A {Unified} {Approach} to {Combinatorial} {Formulas} for {Schubert} {Polynomials}}, volume = {20}, issn = {0925-9899}, url = {http://link.springer.com/10.1023/B:JACO.0000048515.00922.47}, doi = {10.1023/B:JACO.0000048515.00922.47}, abstract = {Schubert polynomials were introduced in the context of the geometry of flag varieties. This paper investigates some of the connections not yet understood between several combinatorial structures for the construction of Schubert polynomials; we also present simplifications in some of the existing approaches to this area. We designate certain line diagrams for permutations known as rc-graphs as the main structure. The other structures in the literature we study include: semistandard Young tableaux, Kohnert diagrams, and balanced labelings of the diagram of a permutation. The main tools in our investigation are certain operations on rc-graphs, which correspond to the coplactic operations on tableaux, and thus define a crystal graph structure on rc-graphs; a new definition of these operations is presented. One application of these operations is a straightforward, purely combinatorial proof of a recent formula (due to Buch, Kresch, Tamvakis, and Yong), which expresses Schubert polynomials in terms of products of Schur polynomials. In spite of the fact that it refers to many objects and results related to them, the paper is mostly self-contained.}, language = {en}, number = {3}, urldate = {2022-09-14}, journal = {Journal of Algebraic Combinatorics}, author = {Lenart, Cristian}, month = nov, year = {2004}, pages = {263--299}, file = {Lenart - 2004 - A Unified Approach to Combinatorial Formulas for S.pdf:/Users/sarahgold/Zotero/storage/ZJDHN69J/Lenart - 2004 - A Unified Approach to Combinatorial Formulas for S.pdf:application/pdf}, } @book{bump_crystal_2017, title = {Crystal bases}, isbn = {978-981-4733-44-1}, url = {https://mathscinet.ams.org/mathscinet-getitem?mr=3642318}, urldate = {2022-09-14}, publisher = {World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ}, author = {Bump, Daniel and Schilling, Anne}, year = {2017}, mrnumber = {3642318}, doi = {10.1142/9876}, annote = {Representations and combinatorics}, file = {MathSciNet Snapshot:/Users/sarahgold/Zotero/storage/TW7HT9TG/mathscinet-getitem.html:text/html}, } @article{lascoux_schubert_1985, title = {Schubert polynomials and the {Littlewood}-{Richardson} rule}, volume = {10}, issn = {0377-9017}, url = {https://mathscinet.ams.org/mathscinet-getitem?mr=815233}, doi = {10.1007/BF00398147}, number = {2-3}, urldate = {2022-09-14}, journal = {Letters in Mathematical Physics. A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics}, author = {Lascoux, Alain and Schützenberger, Marcel-Paul}, year = {1985}, mrnumber = {815233}, pages = {111--124}, file = {MathSciNet Snapshot:/Users/sarahgold/Zotero/storage/T9QCPBC7/mathscinet-getitem.html:text/html}, } @book{bjorner_combinatorics_2005, edition = {1}, series = {Graduate {Texts} in {Mathematics} 231}, title = {Combinatorics of {Coxeter} {Groups}}, isbn = {978-3-540-44238-7}, url = {http://gen.lib.rus.ec/book/index.php?md5=5b11f0221bf145622e1a9624d4170d9d}, urldate = {2022-09-27}, publisher = {Springer-Verlag Berlin Heidelberg}, author = {Bjorner, Anders and Brenti (auth.), Francesco}, year = {2005}, file = {Bjorner and Brenti (auth.) - 2005 - Combinatorics of Coxeter Groups.pdf:/Users/sarahgold/Zotero/storage/38I3B5K9/Bjorner and Brenti (auth.) - 2005 - Combinatorics of Coxeter Groups.pdf:application/pdf}, } @article{mason_explicit_2009, title = {An explicit construction of type {A} {Demazure} atoms}, volume = {29}, issn = {1572-9192}, url = {https://doi.org/10.1007/s10801-008-0133-4}, doi = {10.1007/s10801-008-0133-4}, abstract = {Demazure characters of type A, which are equivalent to key polynomials, have been decomposed by Lascoux and Schützenberger into standard bases. We prove that the resulting polynomials, which we call Demazure atoms, can be obtained from a certain specialization of nonsymmetric Macdonald polynomials. This combinatorial interpretation for Demazure atoms accelerates the computation of the right key associated to a semi-standard Young tableau. Utilizing a related construction, we provide a new combinatorial description of the key polynomials.}, language = {en}, number = {3}, urldate = {2022-10-01}, journal = {Journal of Algebraic Combinatorics}, author = {Mason, S.}, month = may, year = {2009}, keywords = {Demazure characters, Symmetric functions, Young tableaux}, pages = {295--313}, file = {Full Text PDF:/Users/sarahgold/Zotero/storage/U9H3NR3I/Mason - 2009 - An explicit construction of type A Demazure atoms.pdf:application/pdf}, } @article{reiner_key_1995, title = {Key polynomials and a flagged {Littlewood}—{Richardson} rule}, volume = {70}, issn = {00973165}, url = {https://linkinghub.elsevier.com/retrieve/pii/0097316595900837}, doi = {10.1016/0097-3165(95)90083-7}, language = {en}, number = {1}, urldate = {2022-10-01}, journal = {Journal of Combinatorial Theory, Series A}, author = {Reiner, Victor and Shimozono, Mark}, month = apr, year = {1995}, pages = {107--143}, file = {Full Text:/Users/sarahgold/Zotero/storage/IKIXFW9L/Reiner and Shimozono - 1995 - Key polynomials and a flagged Littlewood—Richardso.pdf:application/pdf}, } @article{billey_combinatorial_1993, title = {Some combinatorial properties of {Schubert} polynomials}, volume = {2}, issn = {09259899}, url = {http://link.springer.com/10.1023/A:1022419800503}, doi = {10.1023/A:1022419800503}, number = {4}, urldate = {2022-10-01}, journal = {Journal of Algebraic Combinatorics}, author = {Billey, Sara C. and Jockusch, William and Stanley, Richard P.}, year = {1993}, pages = {345--374}, file = {Full Text:/Users/sarahgold/Zotero/storage/QF6IDQ5N/Billey et al. - 1993 - [No title found].pdf:application/pdf}, } @article{fomin_schubert_1994, title = {Schubert {Polynomials} and the {Nilcoxeter} {Algebra}}, volume = {103}, issn = {00018708}, url = {https://linkinghub.elsevier.com/retrieve/pii/S0001870884710097}, doi = {10.1006/aima.1994.1009}, language = {en}, number = {2}, urldate = {2022-10-01}, journal = {Advances in Mathematics}, author = {Fomin, S. and Stanley, R.P.}, month = feb, year = {1994}, pages = {196--207}, file = {Full Text:/Users/sarahgold/Zotero/storage/2BC74Q8M/Fomin and Stanley - 1994 - Schubert Polynomials and the Nilcoxeter Algebra.pdf:application/pdf}, } @article{joseph_demazure_1985, title = {On the {Demazure} character formula.}, volume = {18}, issn = {0012-9593}, number = {4}, journal = {Ann. Sci. École Norm. Sup.}, author = {Joseph, A.}, year = {1985}, pages = {389--419}, file = {Joseph - 1985 - On the Demazure character formula..pdf:/Users/sarahgold/Zotero/storage/E9EZYZZ5/Joseph - 1985 - On the Demazure character formula..pdf:application/pdf}, } @book{fulton_young_1999, series = {London {Mathematical} {Society} {Student} {Texts} \#35}, title = {Young {Tableaux}: {With} {Applications} to {Representation} {Theory} and {Geometry}}, isbn = {978-0-521-56144-0}, shorttitle = {Young {Tableaux}}, url = {http://gen.lib.rus.ec/book/index.php?md5=7418F1164CA794639DE1BAFCE73CA5CC}, urldate = {2022-10-04}, publisher = {Cambridge University Press}, author = {Fulton, William}, year = {1999}, file = {Fulton - 1999 - Young Tableaux With Applications to Representatio.pdf:/Users/sarahgold/Zotero/storage/AWGGSF2J/Fulton - 1999 - Young Tableaux With Applications to Representatio.pdf:application/pdf}, } @book{shimozono_crystals_2005, title = {Crystals {For} {Dummies}}, url = {http://gen.lib.rus.ec/book/index.php?md5=eecb4dcafb9dd491dccd17d0c03ffc8f}, urldate = {2022-10-04}, author = {Shimozono, Mark}, year = {2005}, file = {Shimozono - 2005 - Crystals For Dummies.pdf:/Users/sarahgold/Zotero/storage/MHJELNVT/Shimozono - 2005 - Crystals For Dummies.pdf:application/pdf}, } @book{heubach_combinatorics_2009, series = {Discrete {Mathematics} and {Its} {Applications}}, title = {Combinatorics of {Compositions} and {Words}}, isbn = {978-1-4200-7267-9}, urldate = {2022-10-26}, publisher = {Chapman and Hall}, author = {Heubach, Silvia and Mansour, Toufik}, year = {2009}, file = {Heubach and Mansour - 2009 - Combinatorics of Compositions and Words.pdf:/Users/sarahgold/Zotero/storage/XMULCBIV/Heubach and Mansour - 2009 - Combinatorics of Compositions and Words.pdf:application/pdf}, } @article{assaf_nonsymmetric_2018, title = {Nonsymmetric {Macdonald} polynomials and a refinement of {Kostka}-{Foulkes} polynomials}, volume = {370}, issn = {0002-9947, 1088-6850}, url = {http://arxiv.org/abs/1703.02466}, doi = {10.1090/tran/7374}, abstract = {We study the specialization of the type A nonsymmetric Macdonald polynomials at \$t=0\$ based on the combinatorial formula of Haglund, Haiman, and Loehr. We prove that this specialization expands nonnegatively into the fundamental slide polynomials, introduced by the author and Searles. Using this and weak dual equivalence, we prove combinatorially that this specialization is a positive graded sum of Demazure characters. We use stability results for fundamental slide polynomials to show that this specialization stabilizes and to show that the Demazure character coefficients give a refinement of the Kostka--Foulkes polynomials.}, number = {12}, urldate = {2022-11-02}, journal = {Transactions of the American Mathematical Society}, author = {Assaf, Sami}, month = jul, year = {2018}, keywords = {Mathematics - Combinatorics, Mathematics - Representation Theory}, pages = {8777--8796}, annote = {Comment: 15 pages, 12 figures; expanded introduction and updated references}, file = {arXiv Fulltext PDF:/Users/sarahgold/Zotero/storage/FCZRATAS/Assaf - 2018 - Nonsymmetric Macdonald polynomials and a refinemen.pdf:application/pdf;arXiv.org Snapshot:/Users/sarahgold/Zotero/storage/CPEQ2X7R/1703.html:text/html;Assaf2018 Published Version:/Users/sarahgold/Zotero/storage/J2TG2P3Y/Assaf - 2018 - Nonsymmetric Macdonald polynomials and a refinemen.pdf:application/pdf}, } @article{chen_affine_2021, title = {An {Affine} {Approach} to {Peterson} {Comparison}}, volume = {25}, doi = {10.1007/s10468-021-10075-5}, abstract = {The Peterson comparison formula proved by Woodward relates the three-pointed Gromov-Witten invariants for the quantum cohomology of partial flag varieties to those for the complete flag. Another such comparison can be obtained by composing a combinatorial version of the Peterson isomorphism with a result of Lapointe and Morse relating quantum Littlewood-Richardson coefficients for the Grassmannian to k-Schur analogs in the homology of the affine Grassmannian obtained by adding rim hooks. We show that these comparisons on quantum cohomology are equivalent, up to Postnikov’s strange duality isomorphism.}, journal = {Algebras and Representation Theory}, author = {Chen, Linda and Milićević, Elizabeth and Morse, Jennifer}, month = jul, year = {2021}, file = {Spring Journal Version.pdf:/Users/sarahgold/Zotero/storage/2G9YTSCR/Chen et al. - 2021 - An Affine Approach to Peterson Comparison.pdf:application/pdf;Submitted Version:/Users/sarahgold/Zotero/storage/B5FHMFQ3/Chen et al. - 2021 - An Affine Approach to Peterson Comparison.pdf:application/pdf}, } @article{edelman_balanced_1987, title = {Balanced tableaux}, volume = {63}, issn = {0001-8708}, url = {https://www.sciencedirect.com/science/article/pii/0001870887900636}, doi = {10.1016/0001-8708(87)90063-6}, abstract = {We study a new class of tableaux defined by a certain condition on hook-ranks. Many connections with the classical theory of standard Young tableaux are developed, as well as applications to the problem of enumerating reduced decompositions of permutations in Sn.}, language = {en}, number = {1}, urldate = {2022-12-08}, journal = {Advances in Mathematics}, author = {Edelman, Paul and Greene, Curtis}, month = jan, year = {1987}, pages = {42--99}, file = {ScienceDirect Full Text PDF:/Users/sarahgold/Zotero/storage/9KKWP2HH/Edelman and Greene - 1987 - Balanced tableaux.pdf:application/pdf;ScienceDirect Snapshot:/Users/sarahgold/Zotero/storage/8B4TRICU/0001870887900636.html:text/html}, } @article{knuth_permutations_1970, title = {Permutations, matrices, and generalized {Young} tableaux}, volume = {34}, issn = {0030-8730}, doi = {10.2140/pjm.1970.34.709}, language = {eng}, number = {3}, journal = {Pacific journal of mathematics}, author = {Knuth, Donald}, year = {1970}, note = {Publisher: Pacific Journal of Mathematics, A Non-profit Corporation}, keywords = {05.30}, pages = {709--727}, file = {Full Text:/Users/sarahgold/Zotero/storage/XI7N3CV6/Knuth - 1970 - Permutations, matrices, and generalized Young tabl.pdf:application/pdf}, } @misc{mason_question_2022, title = {Question {About} {Keys}}, author = {Mason, Sarah}, month = dec, year = {2022}, howpublished = "Personal communication" } @article {LS-schuberts, AUTHOR = {Lascoux, Alain and Sch\"{u}tzenberger, Marcel-Paul}, 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}, ISSN = {0249-6291}, MRCLASS = {14M17 (05A10 14N10)}, MRNUMBER = {660739}, } @article {LS-NCschuberts, AUTHOR = {Lascoux, Alain and Sch\"{u}tzenberger, Marcel-Paul}, TITLE = {Noncommutative {S}chubert polynomials}, JOURNAL = {Funktsional. Anal. i Prilozhen.}, FJOURNAL = {Akademiya Nauk SSSR. Funktsional\cprime ny\u{\i} Analiz i ego Prilozheniya}, VOLUME = {23}, YEAR = {1989}, NUMBER = {3}, PAGES = {63--64}, ISSN = {0374-1990}, MRCLASS = {14M15 (05A15 20B30 32M10)}, MRNUMBER = {1026992}, MRREVIEWER = {Piotr Pragacz}, DOI = {10.1007/bf01079531}, URL = {https://doi.org/10.1007/bf01079531}, } @inproceedings {FominKirillov, AUTHOR = {Fomin, Sergey and Kirillov, Anatol N.}, TITLE = {The {Y}ang-{B}axter equation, symmetric functions, and {S}chubert polynomials}, BOOKTITLE = {Proceedings of the 5th {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({F}lorence, 1993)}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {153}, YEAR = {1996}, NUMBER = {1-3}, PAGES = {123--143}, ISSN = {0012-365X}, MRCLASS = {05E05 (14C17 14M15 82B23)}, MRNUMBER = {1394950}, MRREVIEWER = {Jean-Yves Thibon}, DOI = {10.1016/0012-365X(95)00132-G}, URL = {https://doi.org/10.1016/0012-365X(95)00132-G}, } @article {KnutsonMiller, AUTHOR = {Knutson, Allen and Miller, Ezra}, TITLE = {Gr\"{o}bner 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}, ISSN = {0003-486X}, MRCLASS = {05E15 (13C40 13F55 13P10 14M15 14N15)}, MRNUMBER = {2180402}, MRREVIEWER = {Harry Tamvakis}, DOI = {10.4007/annals.2005.161.1245}, URL = {https://doi.org/10.4007/annals.2005.161.1245}, } @article {Borel, AUTHOR = {Borel, Armand}, 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. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {57}, YEAR = {1953}, PAGES = {115--207}, ISSN = {0003-486X}, MRCLASS = {56.0X}, MRNUMBER = {51508}, MRREVIEWER = {S. Chern}, DOI = {10.2307/1969728}, URL = {https://doi.org/10.2307/1969728}, } @article {BGG, 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}, ISSN = {0042-1316}, MRCLASS = {14M15 (57F15)}, MRNUMBER = {0429933}, MRREVIEWER = {George R. Kempf}, } @article {Demazure, AUTHOR = {Demazure, Michel}, TITLE = {D\'{e}singularisation des vari\'{e}t\'{e}s de {S}chubert g\'{e}n\'{e}ralis\'{e}es}, JOURNAL = {Ann. Sci. \'{E}cole Norm. Sup. (4)}, FJOURNAL = {Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure. Quatri\`eme S\'{e}rie}, VOLUME = {7}, YEAR = {1974}, PAGES = {53--88}, ISSN = {0012-9593}, MRCLASS = {14M15 (20G05)}, MRNUMBER = {354697}, MRREVIEWER = {S. I. Gel\cprime fand}, URL = {http://www.numdam.org/item?id=ASENS_1974_4_7_1_53_0}, } @article {KohnertThesis, AUTHOR = {Kohnert, Axel}, TITLE = {Weintrauben, {P}olynome, {T}ableaux}, NOTE = {Dissertation, Universit\"{a}t Bayreuth, Bayreuth, 1990}, JOURNAL = {Bayreuth. Math. Schr.}, FJOURNAL = {Bayreuther Mathematische Schriften}, NUMBER = {38}, YEAR = {1991}, PAGES = {1--97}, ISSN = {0172-1062}, MRCLASS = {05E10 (05A10 05A17 14M15 20C30)}, MRNUMBER = {1132534}, MRREVIEWER = {Volker Strehl}, } @article {Demazure-characters, AUTHOR = {Demazure, Michel}, TITLE = {Une nouvelle formule des caract\`eres}, JOURNAL = {Bull. Sci. Math. (2)}, FJOURNAL = {Bulletin des Sciences Math\'{e}matiques. 2e S\'{e}rie}, VOLUME = {98}, YEAR = {1974}, NUMBER = {3}, PAGES = {163--172}, ISSN = {0007-4497}, MRCLASS = {17B10 (20G05)}, MRNUMBER = {430001}, MRREVIEWER = {S. I. Gel\cprime fand}, } @article {Littelmann, AUTHOR = {Littelmann, Peter}, TITLE = {Crystal graphs and {Y}oung tableaux}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {175}, YEAR = {1995}, NUMBER = {1}, PAGES = {65--87}, ISSN = {0021-8693}, MRCLASS = {17B37 (17B10 17B67)}, MRNUMBER = {1338967}, MRREVIEWER = {Kailash C. Misra}, DOI = {10.1006/jabr.1995.1175}, URL = {https://doi.org/10.1006/jabr.1995.1175}, } @article {Kashiwara, AUTHOR = {Kashiwara, Masaki}, TITLE = {The crystal base and {L}ittelmann's refined {D}emazure character formula}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {71}, YEAR = {1993}, NUMBER = {3}, PAGES = {839--858}, ISSN = {0012-7094}, MRCLASS = {17B37 (17B10 17B67)}, MRNUMBER = {1240605}, MRREVIEWER = {Kailash C. Misra}, DOI = {10.1215/S0012-7094-93-07131-1}, URL = {https://doi.org/10.1215/S0012-7094-93-07131-1}, } @article {Miller, AUTHOR = {Miller, Ezra}, 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}, ISSN = {0097-3165,1096-0899}, MRCLASS = {05E15 (14M15)}, MRNUMBER = {1996064}, MRREVIEWER = {Mikhail\ Kogan}, DOI = {10.1016/S0097-3165(03)00020-7}, URL = {https://doi.org/10.1016/S0097-3165(03)00020-7}, } @article {KashiwaraCrystal, AUTHOR = {Kashiwara, Masaki}, TITLE = {Crystalizing the {$q$}-analogue of universal enveloping algebras}, JOURNAL = {Comm. Math. Phys.}, FJOURNAL = {Communications in Mathematical Physics}, VOLUME = {133}, YEAR = {1990}, NUMBER = {2}, PAGES = {249--260}, ISSN = {0010-3616,1432-0916}, MRCLASS = {17B37 (17B67)}, MRNUMBER = {1090425}, MRREVIEWER = {Kailash\ C.\ Misra}, URL = {http://projecteuclid.org/euclid.cmp/1104201397}, } @article {KnutsonMillerShimozono, AUTHOR = {Knutson, Allen and Miller, Ezra and Shimozono, Mark}, TITLE = {Four positive formulae for type {$A$} quiver polynomials}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {166}, YEAR = {2006}, NUMBER = {2}, PAGES = {229--325}, ISSN = {0020-9910,1432-1297}, MRCLASS = {14M15 (05E15)}, MRNUMBER = {2249801}, MRREVIEWER = {Harry\ Tamvakis}, DOI = {10.1007/s00222-006-0505-0}, URL = {https://doi.org/10.1007/s00222-006-0505-0}, } @article {BuchFulton, AUTHOR = {Buch, Anders Skovsted and Fulton, William}, TITLE = {Chern class formulas for quiver varieties}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {135}, YEAR = {1999}, NUMBER = {3}, PAGES = {665--687}, ISSN = {0020-9910,1432-1297}, MRCLASS = {14N15 (05E10 14C17 14M15)}, MRNUMBER = {1669280}, MRREVIEWER = {Gary\ P.\ Kennedy}, DOI = {10.1007/s002220050297}, URL = {https://doi.org/10.1007/s002220050297}, } @incollection {LS-keys, AUTHOR = {Lascoux, Alain and Sch\"{u}tzenberger, Marcel-Paul}, TITLE = {Keys \& standard bases}, BOOKTITLE = {Invariant theory and tableaux ({M}inneapolis, {MN}, 1988)}, SERIES = {IMA Vol. Math. Appl.}, VOLUME = {19}, PAGES = {125--144}, PUBLISHER = {Springer, New York}, YEAR = {1990}, ISBN = {0-387-97170-X}, MRCLASS = {05E10 (20C30)}, MRNUMBER = {1035493}, MRREVIEWER = {Piotr\ Pragacz}, } @article {LamLeeShimozono, AUTHOR = {Lam, Thomas and Lee, Seung Jin and Shimozono, Mark}, TITLE = {Back stable {S}chubert calculus}, JOURNAL = {Compos. Math.}, FJOURNAL = {Compositio Mathematica}, VOLUME = {157}, YEAR = {2021}, NUMBER = {5}, PAGES = {883--962}, ISSN = {0010-437X,1570-5846}, MRCLASS = {14M15 (05E05)}, MRNUMBER = {4252201}, MRREVIEWER = {Praise\ Adeyemo}, DOI = {10.1112/S0010437X21007028}, URL = {https://doi.org/10.1112/S0010437X21007028}, } @article {StanleySymm, AUTHOR = {Stanley, Richard P.}, 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}, NUMBER = {4}, PAGES = {359--372}, ISSN = {0195-6698,1095-9971}, MRCLASS = {05A15 (17B10 20F10)}, MRNUMBER = {782057}, MRREVIEWER = {Robert\ A.\ Proctor}, DOI = {10.1016/S0195-6698(84)80039-6}, URL = {https://doi.org/10.1016/S0195-6698(84)80039-6}, } @article {Kogan, AUTHOR = {Kogan, Mikhail}, TITLE = {Generalization of {S}chensted insertion algorithm to the cases of hooks and semi-shuffles}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {102}, YEAR = {2003}, NUMBER = {1}, PAGES = {110--135}, ISSN = {0097-3165,1096-0899}, MRCLASS = {05E10 (05E05 14M15)}, MRNUMBER = {1970980}, MRREVIEWER = {Timothy\ Y.\ Chow}, DOI = {10.1016/S0097-3165(03)00022-0}, URL = {https://doi.org/10.1016/S0097-3165(03)00022-0}, }