{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T12:03:37Z","timestamp":1776686617785,"version":"3.51.2"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"03n04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1999,6]]},"abstract":"<jats:p> We introduce the quantum multi\u2013Schur functions, quantum factorial Schur functions and quantum Macdonald polynomials. We prove that for restricted vexillary permutations, the quantum double Schubert polynomial coincides with some quantum multi-Schur function and prove a quantum analog of the N\u00e4gelsbach\u2013Kostka and Jacobi\u2013Trudi formulae for the quantum double Schubert polynomials in the case of Grassmannian permutations. We prove also an analog of the Giambelli and the Billey\u2013Jockusch\u2013Stanley formula for quantum Schubert polynomials. Finally we formulate two conjectures about the structure of quantum double and quantum Schubert polynomials for 321\u2013avoiding permutations. <\/jats:p>","DOI":"10.1142\/s0218196799000242","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:05:54Z","timestamp":1027767954000},"page":"385-404","source":"Crossref","is-referenced-by-count":4,"title":["QUANTUM SCHUBERT POLYNOMIALS AND QUANTUM SCHUR FUNCTIONS"],"prefix":"10.1142","volume":"09","author":[{"given":"ANATOL N.","family":"KIRILLOV","sequence":"first","affiliation":[{"name":"CRM, University of Montreal, C. P. 6128, Succursale A, Montreal (Quebec) H3C\u00a03J7, Canada"},{"name":"Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191011, Russia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022419800503"},{"key":"p_2","first-page":"263","volume":"6","author":"Ciocan-Fontanine I.","year":"1995","journal-title":"Quantum Notes"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1994.1361"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02101846"},{"key":"p_9","first-page":"393","volume":"295","author":"Lascoux A.","year":"1982","journal-title":"Serie I"},{"key":"p_11","first-page":"667","volume":"321","author":"Lascoux A.","year":"1995","journal-title":"Serie I"},{"key":"p_12","first-page":"447","volume":"294","author":"Lascoux A.","year":"1982","journal-title":"Serie I"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0063238"},{"key":"p_14","first-page":"629","volume":"295","author":"Lascoux A.","year":"1982","journal-title":"Serie I"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1007\/BF02881113"},{"key":"p_20","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(84)80039-6"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(85)80052-4"},{"key":"p_22","first-page":"0","volume":"4","author":"Wachs M.","year":"1985","journal-title":"J. Comb. Theory A"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196799000242","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:56:02Z","timestamp":1565128562000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196799000242"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,6]]},"references-count":13,"journal-issue":{"issue":"03n04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1999,6]]}},"alternative-id":["10.1142\/S0218196799000242"],"URL":"https:\/\/doi.org\/10.1142\/s0218196799000242","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,6]]}}}