% Encoding: UTF-8 @book {Abh88, AUTHOR = {Abhyankar, Shreeram S.}, TITLE = {Enumerative combinatorics of {Y}oung tableaux}, SERIES = {Monographs and Textbooks in Pure and Applied Mathematics}, VOLUME = {115}, PUBLISHER = {Marcel Dekker, Inc., New York}, YEAR = {1988}, PAGES = {xx+509}, ISBN = {0-8247-7816-2}, MRCLASS = {05A15 (14M12 15A15 15A72)}, MRREVIEWER = {Joseph Kung}, } @book {BB05, AUTHOR = {Bj\"{o}rner, 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}, ISBN = {978-3540-442387; 3-540-44238-3}, MRCLASS = {05-01 (05E15 20F55)}, MRREVIEWER = {Jian-yi Shi}, } @Article{BB93, author = {Bergeron, Nantel and Billey, Sara}, fjournal = {Experimental Mathematics}, journal = {Experiment. Math.}, title = {{R}{C}-graphs and {S}chubert polynomials}, year = {1993}, number = {4}, pages = {257--269}, volume = {2}, publisher = {Taylor \& Francis}, } @article {BC98, AUTHOR = {Bruns, Winfried and Conca, Aldo}, TITLE = {K{RS} and powers of determinantal ideals}, JOURNAL = {Compos. Math.}, FJOURNAL = {Compositio Mathematica}, VOLUME = {111}, YEAR = {1998}, NUMBER = {1}, PAGES = {111--122}, ISSN = {0010-437X}, MRCLASS = {13C40 (05E10 13A30 13P10)}, MRREVIEWER = {Ngo Viet Trung}, DOI = {10.1023/A:1000287107308}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1023/A:1000287107308}, } @article {Beh08, AUTHOR = {Behrend, Roger E.}, TITLE = {Osculating paths and oscillating tableaux}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {15}, YEAR = {2008}, NUMBER = {1}, PAGES = {Research Paper 7, 60}, MRCLASS = {05A15 (05E10)}, URL = {http://www.combinatorics.org/Volume_15/Abstracts/v15i1r7.html}, } @article {Ber15, AUTHOR = {Bertiger, Anna}, TITLE = {Generating the ideals defining unions of {S}chubert varieties}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2015}, NUMBER = {21}, PAGES = {10847--10858}, ISSN = {1073-7928}, MRCLASS = {14M15 (13P10)}, MRREVIEWER = {Shizuo Kaji}, DOI = {10.1093/imrn/rnu263}, URL = {https://doi-org.proxy.lib.umich.edu/10.1093/imrn/rnu263}, } @article {BGG73, 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{BJS93, author = {Billey, Sara C. and Jockusch, William and Stanley, Richard P.}, fjournal = {Journal of Algebraic Combinatorics}, journal = {J. Algebraic Combin.}, title = {Some combinatorial properties of {S}chubert polynomials}, year = {1993}, number = {4}, pages = {345--374}, volume = {2}, publisher = {Springer US}, } @article {Boo12, AUTHOR = {Boocher, Adam}, TITLE = {Free resolutions and sparse determinantal ideals}, JOURNAL = {Math. Res. Lett.}, FJOURNAL = {Mathematical Research Letters}, VOLUME = {19}, YEAR = {2012}, NUMBER = {4}, PAGES = {805--821}, ISSN = {1073-2780}, MRCLASS = {13D02 (13C40)}, MRREVIEWER = {Toma\v{z} Ko\v{s}ir}, DOI = {10.4310/MRL.2012.v19.n4.a6}, URL = {https://doi-org.ezp3.lib.umn.edu/10.4310/MRL.2012.v19.n4.a6}, } @Article{Bor53, author = {Borel, Armand}, journal = {Ann. of Math. (2)}, title = {Sur la cohomologie des espaces fibr\'{e}s principaux et des espaces homog\`enes de groupes de {L}ie compacts}, year = {1953}, pages = {115--207}, volume = {57}, fjournal = {Annals of Mathematics. Second Series}, } %%%%%%%%%%%%%%%%%%%%%% %No mathscinet entry %%%%%%%%%%%%%%%%%%%%%% @article {BS02, AUTHOR = {Bergeron, Nantel and Sottile, Frank}, TITLE = {A {P}ieri-type formula for isotropic flag manifolds}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {354}, YEAR = {2002}, NUMBER = {7}, PAGES = {2659--2705}, ISSN = {0002-9947}, MRCLASS = {14N15 (05E15 06A07 14M15)}, MRREVIEWER = {Harry Tamvakis}, DOI = {10.1090/S0002-9947-02-02946-X}, URL = {https://doi-org.proxy.lib.umich.edu/10.1090/S0002-9947-02-02946-X}, } @article {BS17, AUTHOR = {Brualdi, Richard A. and Schroeder, Michael W.}, TITLE = {Alternating sign matrices and their {B}ruhat order}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {340}, YEAR = {2017}, NUMBER = {8}, PAGES = {1996--2019}, ISSN = {0012-365X}, MRCLASS = {05B20 (05A05 06A07)}, MRREVIEWER = {Anouar Ben Mabrouk}, DOI = {10.1016/j.disc.2016.10.010}, URL = {https://doi-org.proxy.lib.umich.edu/10.1016/j.disc.2016.10.010}, } @Article{BS20, author = {Buciumas, Valentin and Scrimshaw, Travis}, journal = {International Mathematics Research Notices}, title = {Double {G}rothendieck polynomials and colored lattice models}, year = {2020}, month = dec, doi = {10.1093/imrn/rnaa327}, } @Article{Buc02, author = {Buch, Anders Skovsted}, journal = {Duke Math. J.}, title = {Grothendieck classes of quiver varieties}, year = {2002}, issn = {0012-7094}, number = {1}, pages = {75--103}, volume = {115}, fjournal = {Duke Mathematical Journal}, mrclass = {14C35 (05E10 19E08)}, } @article {BW96, AUTHOR = {Bj\"{o}rner, Anders and Wachs, Michelle L.}, TITLE = {Shellable nonpure complexes and posets. {I}}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {348}, YEAR = {1996}, NUMBER = {4}, PAGES = {1299--1327}, ISSN = {0002-9947}, MRCLASS = {06A08 (05E99 52B99)}, MRREVIEWER = {T. S. Blyth}, DOI = {10.1090/S0002-9947-96-01534-6}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1090/S0002-9947-96-01534-6}, } @article {CD99, AUTHOR = {Conca, Aldo and De Negri, Emanuela}, TITLE = {{$M$}-sequences, graph ideals, and ladder ideals of linear type}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {211}, YEAR = {1999}, NUMBER = {2}, PAGES = {599--624}, ISSN = {0021-8693}, MRCLASS = {13C40 (13H10 13P10)}, MRREVIEWER = {Rafael H. Villarreal}, DOI = {10.1006/jabr.1998.7740}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1006/jabr.1998.7740}, } @misc {CDF+21, AUTHOR = {Celikbas, Ela and Dufresne, Emilie and Fouli, Louiza and Gorla, Elisa and Lin, Kuei-Nuan and Polini, Claudia and Swanson, Irena}, TITLE = {Rees algebras of sparse determinantal ideals}, eprinttype = {arXiv}, eprint = {2101.03222}, YEAR = {2021}, } @article {CDG20, AUTHOR = {Conca, A. and De Negri, E. and Gorla, E.}, TITLE = {Universal {G}r\"{o}bner bases and {C}artwright-{S}turmfels ideals}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2020}, NUMBER = {7}, PAGES = {1979--1991}, ISSN = {1073-7928}, MRCLASS = {13P10}, MRREVIEWER = {C\'{\i}cero Carvalho}, DOI = {10.1093/imrn/rny075}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1093/imrn/rny075}, } @article {CH97, AUTHOR = {Conca, Aldo and Herzog, J\"{u}rgen}, TITLE = {Ladder determinantal rings have rational singularities}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {132}, YEAR = {1997}, NUMBER = {1}, PAGES = {120--147}, ISSN = {0001-8708}, MRCLASS = {13C40 (13A35 13C14 13F50)}, MRREVIEWER = {Irena Swanson}, DOI = {10.1006/aima.1997.1679}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1006/aima.1997.1679}, } @article {CMR20, AUTHOR = {Clarke, Oliver and Mohammadi, Fatemeh and Rauh, Johannes}, TITLE = {Conditional independence ideals with hidden variables}, JOURNAL = {Adv. in Appl. Math.}, FJOURNAL = {Advances in Applied Mathematics}, VOLUME = {117}, YEAR = {2020}, PAGES = {102029, 25}, ISSN = {0196-8858}, MRCLASS = {13C40 (05E40 13H10 13P10 13P25 62R01)}, MRREVIEWER = {Seth Sullivant}, DOI = {10.1016/j.aam.2020.102029}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/j.aam.2020.102029}, } @article {Con95, AUTHOR = {Conca, Aldo}, TITLE = {Ladder determinantal rings}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {98}, YEAR = {1995}, NUMBER = {2}, PAGES = {119--134}, ISSN = {0022-4049}, MRCLASS = {13C40 (14M12)}, MRREVIEWER = {Jaime-Luis Garcia-Roig}, DOI = {10.1016/0022-4049(94)00039-L}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/0022-4049(94)00039-L}, } @article {Con96, AUTHOR = {Conca, Aldo}, TITLE = {Gorenstein ladder determinantal rings}, JOURNAL = {J. London Math. Soc. (2)}, FJOURNAL = {Journal of the London Mathematical Society. Second Series}, VOLUME = {54}, YEAR = {1996}, NUMBER = {3}, PAGES = {453--474}, ISSN = {0024-6107}, MRCLASS = {13C40 (14M12)}, MRREVIEWER = {Jaime-Luis Garcia-Roig}, DOI = {10.1112/jlms/54.3.453}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1112/jlms/54.3.453}, } @article {Con98, AUTHOR = {Conca, Aldo}, TITLE = {Straightening law and powers of determinantal ideals of {H}ankel matrices}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {138}, YEAR = {1998}, NUMBER = {2}, PAGES = {263--292}, ISSN = {0001-8708}, MRCLASS = {13C40 (13A30 13F50 13H10)}, MRREVIEWER = {Rafael S\'{a}nchez}, DOI = {10.1006/aima.1998.1740}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1006/aima.1998.1740}, } @Article{CT13, author = {Co\c{s}kun, Olcay and Ta\c{s}k{\i}n, M\"{u}ge}, journal = {J. Combin. Theory Ser. A}, title = {Tower tableaux and {S}chubert polynomials}, year = {2013}, issn = {0097-3165}, number = {8}, pages = {1976--1995}, volume = {120}, doi = {10.1016/j.jcta.2013.08.001}, fjournal = {Journal of Combinatorial Theory. Series A}, mrclass = {05E05}, mrreviewer = {Markus E. Fulmek}, url = {https://doi-org.proxy.lib.umich.edu/10.1016/j.jcta.2013.08.001}, } @article {CV20, AUTHOR = {Conca, Aldo and Varbaro, Matteo}, TITLE = {Square-free {G}r\"{o}bner degenerations}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {221}, YEAR = {2020}, NUMBER = {3}, PAGES = {713--730}, ISSN = {0020-9910}, MRCLASS = {13P10}, DOI = {10.1007/s00222-020-00958-7}, URL = {https://doi-org.proxy.lib.umich.edu/10.1007/s00222-020-00958-7}, } @article {Dem74, 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)}, MRREVIEWER = {S. I. Gel\cprime fand}, URL = {http://www.numdam.org/item?id=ASENS_1974_4_7_1_53_0}, } @article {Din11, AUTHOR = {Dinh Nam, Le}, TITLE = {The determinantal ideals of extended {H}ankel matrices}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {215}, YEAR = {2011}, NUMBER = {6}, PAGES = {1502--1515}, ISSN = {0022-4049}, MRCLASS = {13C40 (13H10 13P10)}, MRREVIEWER = {P. Schenzel}, DOI = {10.1016/j.jpaa.2010.09.008}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/j.jpaa.2010.09.008}, } @article {DL81, AUTHOR = {De Concini, C. and Lakshmibai, V.}, TITLE = {Arithmetic {C}ohen-{M}acaulayness and arithmetic normality for {S}chubert varieties}, JOURNAL = {Amer. J. Math.}, FJOURNAL = {American Journal of Mathematics}, VOLUME = {103}, YEAR = {1981}, NUMBER = {5}, PAGES = {835--850}, ISSN = {0002-9327}, MRCLASS = {14M15 (13H10 14M05)}, MRREVIEWER = {H. H. Andersen}, DOI = {10.2307/2374249}, URL = {https://doi-org.ezp3.lib.umn.edu/10.2307/2374249}, } @article {Dom99, AUTHOR = {Domokos, M\'{a}ty\'{a}s}, TITLE = {Gr\"{o}bner bases of certain determinantal ideals}, JOURNAL = {Beitr\"{a}ge Algebra Geom.}, FJOURNAL = {Beitr\"{a}ge zur Algebra und Geometrie. Contributions to Algebra and Geometry}, VOLUME = {40}, YEAR = {1999}, NUMBER = {2}, PAGES = {479--493}, ISSN = {0138-4821}, MRCLASS = {13C40 (13P10)}, MRREVIEWER = {Franz Pauer}, } @article {EHH13, AUTHOR = {Ene, Viviana and Herzog, J\"{u}rgen and Hibi, Takayuki and Mohammadi, Fatemeh}, TITLE = {Determinantal facet ideals}, JOURNAL = {Michigan Math. J.}, FJOURNAL = {Michigan Mathematical Journal}, VOLUME = {62}, YEAR = {2013}, NUMBER = {1}, PAGES = {39--57}, ISSN = {0026-2285}, MRCLASS = {13C40 (13F55 13P10 15A15 52B12)}, MRREVIEWER = {Toma\v{z} Ko\v{s}ir}, DOI = {10.1307/mmj/1363958240}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1307/mmj/1363958240}, } @Book{Eis95, author = {Eisenbud, David}, publisher = {Springer-Verlag, New York}, title = {Commutative {A}lgebra: with a view toward algebraic geometry}, year = {1995}, } @Article{FGRS97, author = {Fomin, Sergey and Greene, Curtis and Reiner, Victor and Shimozono, Mark}, journal = {European J. Combin.}, title = {Balanced labellings and {S}chubert polynomials}, year = {1997}, issn = {0195-6698}, number = {4}, pages = {373--389}, volume = {18}, doi = {10.1006/eujc.1996.0109}, fjournal = {European Journal of Combinatorics}, mrclass = {05E10 (05E05 05E15)}, mrreviewer = {Witold Kra\'{s}kiewicz}, url = {https://doi-org.proxy.lib.umich.edu/10.1006/eujc.1996.0109}, } @misc{FGS18, title={Bumpless pipedreams, reduced word tableaux and {S}tanley symmetric functions}, author={Fan, Neil JY and Guo, Peter L and Sun, Sophie CC}, eprint={1810.11916}, eprinttype = {arXiv}, year={2018}, } @article {FK20, AUTHOR = {Fieldsteel, Nathan and Klein, Patricia}, TITLE = {Gr\"{o}bner bases and the {C}ohen-{M}acaulay property of {L}i's double determinantal varieties}, JOURNAL = {Proc. Amer. Math. Soc. Ser. B}, FJOURNAL = {Proceedings of the American Mathematical Society. Series B}, VOLUME = {7}, YEAR = {2020}, PAGES = {142--158}, MRCLASS = {14M12 (05E40 13C40 13P10 14M06)}, DOI = {10.1090/bproc/56}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1090/bproc/56}, } @incollection {FK94, AUTHOR = {Fomin, Sergey and Kirillov, Anatol N.}, 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}, MRCLASS = {05E05 (14N15)}, } @Article{FK96, author = {Fomin, Sergey and Kirillov, Anatol N.}, journal = {Discrete Mathematics}, title = {The {Y}ang-{B}axter equation, symmetric functions, and {S}chubert polynomials}, year = {1996}, number = {1-3}, pages = {123--143}, volume = {153}, publisher = {Elsevier}, } @Article{FMS21, author = {Fink, Alex and M\'{e}sz\'{a}ros, Karola and St. Dizier, Avery}, journal = {Math. Z.}, title = {Zero-one {S}chubert polynomials}, year = {2021}, issn = {0025-5874}, number = {3-4}, pages = {1023--1042}, volume = {297}, doi = {10.1007/s00209-020-02544-2}, fjournal = {Mathematische Zeitschrift}, mrclass = {14N15 (05E14)}, url = {https://doi-org.proxy.lib.umich.edu/10.1007/s00209-020-02544-2}, } @Article{FR03, author = {Feh\'{e}r, L\'{a}szl\'{o} M. and Rim\'{a}nyi, Rich\'{a}rd}, journal = {Cent. Eur. J. Math.}, title = {Schur and {S}chubert polynomials as {T}hom polynomials --- cohomology of moduli spaces}, year = {2003}, issn = {1895-1074}, number = {4}, pages = {418--434}, volume = {1}, doi = {10.2478/BF02475176}, fjournal = {Central European Journal of Mathematics}, mrclass = {05E15 (14C17 14M15)}, mrreviewer = {Harry Tamvakis}, url = {https://doi-org.proxy.lib.umich.edu/10.2478/BF02475176}, } @Article{FS94, author = {Fomin, Sergey and Stanley, Richard P.}, journal = {Adv. Math.}, title = {Schubert polynomials and the nil-{C}oxeter algebra}, year = {1994}, number = {2}, pages = {196--207}, volume = {103}, fjournal = {Advances in Mathematics}, } @Article{Ful92, author = {Fulton, William}, journal = {Duke Math. J.}, title = {Flags, {S}chubert polynomials, degeneracy loci, and determinantal formulas}, year = {1992}, number = {3}, pages = {381--420}, volume = {65}, fjournal = {Duke Mathematical Journal}, } @article{Gho02, AUTHOR = {Sudhir R. Ghorpade}, title = {Hilbert functions of ladder determinantal varieties}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, volume = {246}, number = {1}, pages = {131-175}, year = {2002}, note = {Formal Power Series and Algebraic Combinatorics 1999}, issn = {0012-365X}, doi = {https://doi.org/10.1016/S0012-365X(01)00256-4}, url = {https://www.sciencedirect.com/science/article/pii/S0012365X01002564}, } @article {GL00, AUTHOR = {Gonciulea, N. and Lakshmibai, V.}, TITLE = {Singular loci of ladder determinantal varieties and {S}chubert varieties}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {229}, YEAR = {2000}, NUMBER = {2}, PAGES = {463--497}, ISSN = {0021-8693}, MRCLASS = {14M12 (14M15)}, MRREVIEWER = {Harry Tamvakis}, DOI = {10.1006/jabr.1999.8087}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1006/jabr.1999.8087}, } @article {GL96, AUTHOR = {Gonciulea, N. and Lakshmibai, V.}, TITLE = {Degenerations of flag and {S}chubert varieties to toric varieties}, JOURNAL = {Transform. Groups}, FJOURNAL = {Transformation Groups}, VOLUME = {1}, YEAR = {1996}, NUMBER = {3}, PAGES = {215--248}, ISSN = {1083-4362}, MRCLASS = {14M15 (14M25)}, MRREVIEWER = {E. Aky\i ld\i z}, DOI = {10.1007/BF02549207}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1007/BF02549207}, } @article {GL97, AUTHOR = {Gonciulea, N. and Lakshmibai, V.}, TITLE = {Schubert varieties, toric varieties, and ladder determinantal varieties}, JOURNAL = {Ann. Inst. Fourier (Grenoble)}, FJOURNAL = {Universit\'{e} de Grenoble. Annales de l'Institut Fourier}, VOLUME = {47}, YEAR = {1997}, NUMBER = {4}, PAGES = {1013--1064}, ISSN = {0373-0956}, MRCLASS = {14M25 (14M12 14M15)}, MRREVIEWER = {E. Aky\i ld\i z}, URL = {http://www.numdam.org.ezp3.lib.umn.edu/item?id=AIF_1997__47_4_1013_0}, } @article {GM00, AUTHOR = {Gonciulea, Nicolae and Miller, Claudia}, TITLE = {Mixed ladder determinantal varieties}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {231}, YEAR = {2000}, NUMBER = {1}, PAGES = {104--137}, ISSN = {0021-8693}, MRCLASS = {14M12 (14M15)}, MRREVIEWER = {Paulo F. Machado}, DOI = {10.1006/jabr.2000.8358}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1006/jabr.2000.8358}, } @article {GMN13, AUTHOR = {Gorla, Elisa and Migliore, Juan C. and Nagel, Uwe}, TITLE = {Gr\"{o}bner bases via linkage}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {384}, YEAR = {2013}, PAGES = {110--134}, ISSN = {0021-8693}, MRCLASS = {13C40 (13P10 14M06 14M12 58A17)}, MRREVIEWER = {P. Schenzel}, DOI = {10.1016/j.jalgebra.2013.02.017}, URL = {https://doi-org.proxy.lib.umich.edu/10.1016/j.jalgebra.2013.02.017}, } @article {Gor07, AUTHOR = {Gorla, Elisa}, TITLE = {Mixed ladder determinantal varieties from two-sided ladders}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {211}, YEAR = {2007}, NUMBER = {2}, PAGES = {433--444}, ISSN = {0022-4049}, MRCLASS = {13C40 (14M05 14M06 14M12)}, MRREVIEWER = {Marta Casanellas}, DOI = {10.1016/j.jpaa.2007.01.016}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/j.jpaa.2007.01.016}, } @article {GS95, AUTHOR = {Glassbrenner, Donna and Smith, Karen E.}, TITLE = {Singularities of certain ladder determinantal varieties}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {101}, YEAR = {1995}, NUMBER = {1}, PAGES = {59--75}, ISSN = {0022-4049}, MRCLASS = {13C40 (13H10 14M12)}, MRREVIEWER = {J\"{u}rgen Herzog}, DOI = {10.1016/0022-4049(94)00038-K}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/0022-4049(94)00038-K}, } @article {HE71, AUTHOR = {Hochster, M. and Eagon, John A.}, TITLE = {Cohen-{M}acaulay rings, invariant theory, and the generic perfection of determinantal loci}, JOURNAL = {Amer. J. Math.}, FJOURNAL = {American Journal of Mathematics}, VOLUME = {93}, YEAR = {1971}, PAGES = {1020--1058}, ISSN = {0002-9327}, MRCLASS = {13H10 (14D20 14M05)}, MRREVIEWER = {L. J. Ratliff, Jr.}, DOI = {10.2307/2373744}, URL = {https://doi-org.ezp3.lib.umn.edu/10.2307/2373744}, } @article {HL82, AUTHOR = {Huneke, C. and Lakshmibai, V.}, TITLE = {On the normality of the rings of {S}chubert varieties}, JOURNAL = {Proc. Indian Acad. Sci. Math. Sci.}, FJOURNAL = {Indian Academy of Sciences. Proceedings. Mathematical Sciences}, VOLUME = {91}, YEAR = {1982}, NUMBER = {1}, PAGES = {65--71}, ISSN = {0253-4142}, MRCLASS = {14M15 (14L35 14M17)}, MRREVIEWER = {H. H. Andersen}, DOI = {10.1007/BF02837262}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1007/BF02837262}, } @article {Hoc73, AUTHOR = {Hochster, M.}, TITLE = {Grassmannians and their {S}chubert subvarieties are arithmetically {C}ohen-{M}acaulay}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {25}, YEAR = {1973}, PAGES = {40--57}, ISSN = {0021-8693}, MRCLASS = {13H10 (14M05 14M15 14N10)}, MRREVIEWER = {L. J. Ratliff, Jr.}, DOI = {10.1016/0021-8693(73)90074-4}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/0021-8693(73)90074-4}, } @article {HPW, AUTHOR = {Hamaker, Zachary and Pechenik, Oliver and Weigandt, Anna}, TITLE = {Gr\"{o}bner geometry of {S}chubert polynomials through ice}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {398}, YEAR = {2022}, PAGES = {Paper No. 108228}, ISSN = {0001-8708}, MRCLASS = {Prelim}, MRNUMBER = {4379747}, DOI = {10.1016/j.aim.2022.108228}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/j.aim.2022.108228}, } @article {HT92, AUTHOR = {Herzog, J\"{u}rgen and Trung, Ng\^{o} Vi\^{e}t}, TITLE = {Gr\"{o}bner bases and multiplicity of determinantal and {P}faffian ideals}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {96}, YEAR = {1992}, NUMBER = {1}, PAGES = {1--37}, ISSN = {0001-8708}, MRCLASS = {13D40 (06A08 14M12)}, MRREVIEWER = {P. Schenzel}, DOI = {10.1016/0001-8708(92)90050-U}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/0001-8708(92)90050-U}, } @article{Hua20, title={Bijective Proofs of {M}onk's rule for {S}chubert and Double {S}chubert Polynomials with Bumpless Pipe Dreams}, author={Huang, Daoji}, journal={{\sf arXiv:2010.15048}}, year={2020}, pages={12 pages}, } @article{Hua21, title={Schubert Products for Permutations with Separated Descents}, author={Huang, Daoji}, journal={{\sf arXiv:2105.01591}}, year={2021}, pages={18 pages}, } @article {Hud14, 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 {Ion11, AUTHOR = {Ionov, Boyan}, TITLE = {Initial complex associated to a jet scheme of a determinantal variety}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {215}, YEAR = {2011}, NUMBER = {5}, PAGES = {806--811}, ISSN = {0022-4049}, MRCLASS = {14M12 (13F55 13H10 14M05)}, MRREVIEWER = {Margherita Barile}, DOI = {10.1016/j.jpaa.2010.06.025}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/j.jpaa.2010.06.025}, } @article {Jos84, AUTHOR = {Joseph, Anthony}, TITLE = {On the variety of a highest weight module}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {88}, YEAR = {1984}, NUMBER = {1}, PAGES = {238--278}, } @article {JW07, AUTHOR = {Jonsson, Jakob and Welker, Volkmar}, TITLE = {A spherical initial ideal for {P}faffians}, JOURNAL = {Illinois J. Math.}, FJOURNAL = {Illinois Journal of Mathematics}, VOLUME = {51}, YEAR = {2007}, NUMBER = {4}, PAGES = {1397--1407}, ISSN = {0019-2082}, MRCLASS = {13C40 (05E99 13F55)}, MRREVIEWER = {Margherita Barile}, URL = {http://projecteuclid.org.ezp3.lib.umn.edu/euclid.ijm/1258138551}, } @Article{Kle, author = {Klein, Patricia}, journal = {Preprint}, title = {Degenerations of matrix {S}chubert varieties}, year = {2020}, note = {{\sf arXiv:2008.01717}}, pages = {18 pages}, } @incollection {KM00, AUTHOR = {Kirillov, Anatol N. and Maeno, Toshiaki}, TITLE = {Quantum double {S}chubert polynomials, quantum {S}chubert polynomials and {V}afa-{I}ntriligator formula}, NOTE = {Formal power series and algebraic combinatorics (Vienna, 1997)}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {217}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {191--223}, } @Article{KM05, author = {Knutson, Allen and Miller, Ezra}, fjournal = {Annals of Mathematics}, journal = {Ann. of Math. (2)}, title = {Gr{\"o}bner geometry of {S}chubert polynomials}, year = {2005}, pages = {1245--1318}, publisher = {JSTOR}, } @article {KMS06, 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}, } @Article{KMY09, author = {Knutson, Allen and Miller, Ezra and Yong, Alexander}, journal = {J. Reine Angew. Math.}, title = {Gr\"{o}bner geometry of vertex decompositions and of flagged tableaux}, year = {2009}, pages = {1--31}, volume = {630}, doi = {10.1515/crelle.2009.033}, fjournal = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's Journal]}, } @Article{Knu09, author = {Knutson, Allen}, journal = {Preprint}, title = {Frobenius splitting, point-counting, and degeneration}, year = {2009}, note = {{\sf arXiv:0911.4941}}, pages = {28 pages}, } @misc{Knu19, author = {Knutson, Allen}, title = {Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula}, year = {2019}, eprint={1909.13777}, eprinttype = {arXiv}, } @book {Kog00, AUTHOR = {Kogan, Mikhail}, TITLE = {Schubert geometry of flag varieties and {G}elfand-{C}etlin theory}, NOTE = {Thesis (Ph.D.)--Massachusetts Institute of Technology}, YEAR = {2000}, PAGES = {(no paging)}, MRCLASS = {Thesis}, } @article{KR, title={Geometric vertex decomposition and liaison}, volume={9}, DOI={10.1017/fms.2021.53}, fjournal={Forum of Mathematics, Sigma}, journal = {Forum Math. Sigma}, publisher={Cambridge University Press}, author={Klein, Patricia and Rajchgot, Jenna}, year={2021}, pages={e70}} @article {KV97, AUTHOR = {Kohnert, Axel and Veigneau, S\'{e}bastien}, TITLE = {Using {S}chubert basis to compute with multivariate polynomials}, JOURNAL = {Adv. in Appl. Math.}, FJOURNAL = {Advances in Applied Mathematics}, VOLUME = {19}, YEAR = {1997}, NUMBER = {1}, PAGES = {45--60}, ISSN = {0196-8858}, MRCLASS = {05E15 (05E05)}, DOI = {10.1006/aama.1997.0526}, URL = {https://doi-org.proxy.lib.umich.edu/10.1006/aama.1997.0526}, } @article {KY04, AUTHOR = {Knutson, Allen and Yong, Alexander}, TITLE = {A formula for {$K$}-theory truncation {S}chubert calculus}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices}, YEAR = {2004}, NUMBER = {70}, PAGES = {3741--3756}, ISSN = {1073-7928}, MRCLASS = {14M15 (14C35 19E08)}, MRREVIEWER = {Xuhua He}, DOI = {10.1155/S1073792804142244}, URL = {https://doi-org.proxy.lib.umich.edu/10.1155/S1073792804142244}, } @Article{Las, author = {Lascoux, Alain}, journal = {Preprint}, title = {{C}hern and {Y}ang through ice}, year = {2002}, pages = {17 pages}, } @incollection {Las01, 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}, } @article {Len03, AUTHOR = {Lenart, Cristian}, TITLE = {A {$K$}-theory version of {M}onk's formula and some related multiplication formulas}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {179}, YEAR = {2003}, NUMBER = {1-2}, PAGES = {137--158}, } @Article{Len04, author = {Lenart, Cristian}, journal = {J. Algebraic Combin.}, title = {A unified approach to combinatorial formulas for {S}chubert polynomials}, year = {2004}, number = {3}, pages = {263--299}, volume = {20}, fjournal = {Journal of Algebraic Combinatorics. An International Journal}, } @Article{LLS21, author = {Lam, Thomas and Lee, Seung Jin and Shimozono, Mark}, journal = {Compos. Math.}, title = {Back stable {S}chubert calculus}, year = {2021}, issn = {0010-437X}, number = {5}, pages = {883--962}, volume = {157}, doi = {10.1112/S0010437X21007028}, fjournal = {Compositio Mathematica}, mrclass = {14M15 (05E05)}, url = {https://doi-org.proxy.lib.umich.edu/10.1112/S0010437X21007028}, } @Article{LS82, author = {Lascoux, Alain and Sch{\"u}tzenberger, Marcel-Paul}, journal = {C.R. Acad. Sci. Paris S{\'e}r. I Math}, title = {Polyn\^{o}mes de {S}chubert}, year = {1982}, number = {3}, pages = {447--450}, volume = {295}, } @article {LS85, AUTHOR = {Lascoux, Alain and Sch\"{u}tzenberger, Marcel-Paul}, TITLE = {Schubert polynomials and the {L}ittlewood-{R}ichardson 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{LS96, author = {Lascoux, Alain and Sch\"{u}tzenberger, Marcel-Paul}, journal = {Electron. J. Combin.}, title = {Treillis et bases des groupes de {C}oxeter}, year = {1996}, number = {2}, pages = {Research paper 27, 35}, volume = {3}, fjournal = {Electronic Journal of Combinatorics}, } @article {LY12, AUTHOR = {Li, Li and Yong, Alexander}, TITLE = {Some degenerations of {K}azhdan-{L}usztig ideals and multiplicities of {S}chubert varieties}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {229}, YEAR = {2012}, NUMBER = {1}, PAGES = {633--667}, ISSN = {0001-8708}, MRCLASS = {14M15 (05E15 13P10 14N15)}, MRREVIEWER = {Changzheng Li}, DOI = {10.1016/j.aim.2011.09.010}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/j.aim.2011.09.010}, } @Misc{M2, author = {Grayson, Daniel R. and Stillman, Michael E.}, title = {Macaulay2, a software system for research in algebraic geometry, available at http://www.math.uiuc.edu/{M}acaulay2/}, } @Book{Mac91, author = {Macdonald, Ian Grant}, publisher = {Montr{\'e}al: D{\'e}p. de math{\'e}matique et d'informatique, Universit{\'e} du Qu{\'e}bec {\`a} Montr{\'e}al}, title = {Notes on {S}chubert polynomials}, year = {1991}, volume = {6}, } @Book{Man01, author = {Manivel, Laurent}, publisher = {American Mathematical Soc.}, title = {Symmetric functions, {S}chubert polynomials, and degeneracy loci}, year = {2001}, number = {3}, } @article {MR85, AUTHOR = {Mehta, V. B. and Ramanathan, A.}, TITLE = {Frobenius splitting and cohomology vanishing for {S}chubert varieties}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {122}, YEAR = {1985}, NUMBER = {1}, PAGES = {27--40}, ISSN = {0003-486X}, MRCLASS = {14M15 (20G10)}, MRREVIEWER = {H. H. Andersen}, DOI = {10.2307/1971368}, URL = {https://doi-org.ezp3.lib.umn.edu/10.2307/1971368}, } @Book{MS04, author = {Miller, Ezra and Sturmfels, Bernd}, publisher = {Springer Science \& Business Media}, title = {Combinatorial Commutative Algebra}, year = {2004}, volume = {227}, } @incollection {MS83, AUTHOR = {Musili, C. and Seshadri, C. S.}, TITLE = {Schubert varieties and the variety of complexes}, BOOKTITLE = {Arithmetic and geometry, {V}ol. {II}}, SERIES = {Progr. Math.}, VOLUME = {36}, PAGES = {329--359}, PUBLISHER = {Birkh\"{a}user Boston, Boston, MA}, YEAR = {1983}, MRCLASS = {14M15 (14L30)}, MRREVIEWER = {H. H. Andersen}, } @article {MS89, AUTHOR = {Mehta, V. B. and Srinivas, V.}, TITLE = {A note on {S}chubert varieties in {$G/B$}}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {284}, YEAR = {1989}, NUMBER = {1}, PAGES = {1--5}, ISSN = {0025-5831}, MRCLASS = {14M15 (14L30)}, MRREVIEWER = {Michel Brion}, DOI = {10.1007/BF01443500}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1007/BF01443500}, } @article {MS96, AUTHOR = {Motwani, J. V. and Sohoni, M. A.}, TITLE = {Divisor class groups of ladder determinantal varieties}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {186}, YEAR = {1996}, NUMBER = {2}, PAGES = {338--367}, ISSN = {0021-8693}, MRCLASS = {13C40 (13C20)}, MRREVIEWER = {Aldo Conca}, DOI = {10.1006/jabr.1996.0377}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1006/jabr.1996.0377}, } @article{Nar86, title = {The irreducibility of ladder determinantal varieties}, journal = {Journal of Algebra}, volume = {102}, number = {1}, pages = {162-185}, year = {1986}, issn = {0021-8693}, doi = {https://doi.org/10.1016/0021-8693(86)90134-1}, url = {https://www.sciencedirect.com/science/article/pii/0021869386901341}, author = {Himanee Narasimhan} } @article {Ram85, AUTHOR = {Ramanathan, A.}, TITLE = {Schubert varieties are arithmetically {C}ohen-{M}acaulay}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {80}, YEAR = {1985}, NUMBER = {2}, PAGES = {283--294}, ISSN = {0020-9910}, MRCLASS = {14M15 (14L30)}, MRREVIEWER = {H. H. Andersen}, DOI = {10.1007/BF01388607}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1007/BF01388607}, } @article {Ram87, AUTHOR = {Ramanathan, A.}, TITLE = {Equations defining {S}chubert varieties and {F}robenius splitting of diagonals}, JOURNAL = {Inst. Hautes \'{E}tudes Sci. Publ. Math.}, FJOURNAL = {Institut des Hautes \'{E}tudes Scientifiques. Publications Math\'{e}matiques}, NUMBER = {65}, YEAR = {1987}, PAGES = {61--90}, ISSN = {0073-8301}, MRCLASS = {14M15 (14L40 14M17)}, MRREVIEWER = {E. Aky\i ld\i z}, URL = {http://www.numdam.org.ezp3.lib.umn.edu/item?id=PMIHES_1987__65__61_0}, } @article {Rea02, 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}, ISSN = {0167-8094}, MRCLASS = {05E15 (06A07 20F55)}, MRREVIEWER = {Hiroshi Naruse}, DOI = {10.1023/A:1015287106470}, URL = {https://doi-org.proxy.lib.umich.edu/10.1023/A:1015287106470}, } @incollection {Ros89, AUTHOR = {Rossmann, W.}, TITLE = {Equivariant multiplicities on complex varieties}, NOTE = {Orbites unipotentes et repr\'{e}sentations, III}, JOURNAL = {Ast\'{e}risque}, FJOURNAL = {Ast\'{e}risque}, NUMBER = {173-174}, YEAR = {1989}, PAGES = {11, 313--330}, ISSN = {0303-1179}, MRCLASS = {32M05 (32S20 32S70)}, } @article {RRR+21, AUTHOR = {Rajchgot, Jenna and Ren, Yi and Robichaux, Colleen and St. Dizier, Avery and Weigandt, Anna}, TITLE = {Degrees of symmetric {G}rothendieck polynomials and {C}astelnuovo-{M}umford regularity}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {149}, YEAR = {2021}, NUMBER = {4}, PAGES = {1405--1416}, ISSN = {0002-9939}, MRCLASS = {13C40 (05E40 14N15)}, DOI = {10.1090/proc/15294}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1090/proc/15294}, } @article {Rub05, AUTHOR = {Rubey, Martin}, TITLE = {The {$h$}-vector of a ladder determinantal ring cogenerated by {$2\times 2$} minors is log-concave}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {292}, YEAR = {2005}, NUMBER = {2}, PAGES = {303--323}, ISSN = {0021-8693}, MRCLASS = {05E99 (13A02 13C40)}, MRREVIEWER = {Ilse Fischer}, DOI = {10.1016/j.jalgebra.2005.07.023}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/j.jalgebra.2005.07.023}, } @Manual{sagemath, title = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion 9.2)}, author = {{The Sage Developers}}, note = {{\tt https://www.sagemath.org}}, year = {2021}, key = {SageMath}, } @book {Sch79, AUTHOR = {Schubert, Hermann}, TITLE = {Kalk\"{u}l der abz\"{a}hlenden {G}eometrie}, NOTE = {Reprint of the 1879 original, With an introduction by Steven L. Kleiman}, PUBLISHER = {Springer-Verlag, Berlin-New York}, YEAR = {1979}, PAGES = {349}, } @article {SSS19, AUTHOR = {Sather-Wagstaff, Keri and Se, Tony and Spiroff, Sandra}, TITLE = {Semidualizing modules of {$2\times 2$} ladder determinantal rings}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {538}, YEAR = {2019}, PAGES = {232--252}, ISSN = {0021-8693}, MRCLASS = {13C20 (13B30 13C40)}, MRREVIEWER = {Dana T. Weston}, DOI = {10.1016/j.jalgebra.2019.07.030}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/j.jalgebra.2019.07.030}, } @book {Sta96, AUTHOR = {Stanley, Richard P.}, TITLE = {Combinatorics and commutative algebra}, SERIES = {Progress in Mathematics}, VOLUME = {41}, EDITION = {Second}, PUBLISHER = {Birkh\"{a}user Boston, Inc., Boston, MA}, YEAR = {1996}, PAGES = {x+164}, ISBN = {0-8176-3836-9}, MRCLASS = {05-02 (13F50)}, } @article {Sul08, AUTHOR = {Sullivant, Seth}, TITLE = {Combinatorial symbolic powers}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {319}, YEAR = {2008}, NUMBER = {1}, PAGES = {115--142}, ISSN = {0021-8693}, MRCLASS = {13A15 (05E99 13C40 13P10)}, MRREVIEWER = {Benjamin P. Richert}, DOI = {10.1016/j.jalgebra.2007.09.024}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/j.jalgebra.2007.09.024}, } @article {Wan03, AUTHOR = {Wang, Hsin-Ju}, TITLE = {A determinantal formula for the {H}ilbert series of determinantal rings of one-sided ladder}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {265}, YEAR = {2003}, NUMBER = {1}, PAGES = {79--99}, ISSN = {0021-8693}, MRCLASS = {13C40 (13D40)}, MRREVIEWER = {Ralf Fr\"{o}berg}, DOI = {10.1016/S0021-8693(03)00223-0}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1016/S0021-8693(03)00223-0}, } @misc{Wei, author = {Weigandt, Anna}, title = {Prism tableaux for alternating sign matrix varieties}, year = {2017}, eprint = {1708.07236}, eprinttype = {arXiv}, } @article {Wei21, AUTHOR = {Weigandt, Anna}, TITLE = {Bumpless pipe dreams and alternating sign matrices}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {182}, YEAR = {2021}, PAGES = {105470}, ISSN = {0097-3165}, DOI = {10.1016/j.jcta.2021.105470}, } @article {WY06, AUTHOR = {Woo, Alexander and Yong, Alexander}, TITLE = {When is a {S}chubert variety {G}orenstein?}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {207}, YEAR = {2006}, NUMBER = {1}, PAGES = {205--220}, } @article {WY12, AUTHOR = {Woo, Alexander and Yong, Alexander}, TITLE = {A {G}r\"{o}bner basis for {K}azhdan-{L}usztig ideals}, JOURNAL = {Amer. J. Math.}, FJOURNAL = {American Journal of Mathematics}, VOLUME = {134}, YEAR = {2012}, NUMBER = {4}, PAGES = {1089--1137}, ISSN = {0002-9327}, MRCLASS = {14M15 (13P10)}, MRREVIEWER = {Venkatramani Lakshmibai}, DOI = {10.1353/ajm.2012.0031}, URL = {https://doi-org.ezp3.lib.umn.edu/10.1353/ajm.2012.0031}, } @Article{YSlides, author = {Yong, Alexander}, journal = {Slides}, title = {Gr\"obner geometry of geometric vertex decompositions}, year = {2004}, } @Comment{jabref-meta: databaseType:bibtex;} @Comment{jabref-meta: saveOrderConfig:specified;citationkey;false;author;false;title;true;}