On q-integrals over order polytopes

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• 作者：Jang Soo Kim^a ; ^{jangsookim@skku.edu} ; Dennis Stanton^b ; ^{stanton@math.umn.edu}
• 关键词：primary ; 05A30 ; secondary ; 05A15 ; 06A07
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：21 February 2017
• 年：2017
• 卷：308
• 期：Complete
• 页码：1269-1317
• 全文大小：820 K
• 卷排序：308

文摘

A combinatorial study of multiple q-integrals is developed. This includes a q-volume of a convex polytope, which depends upon the order of q-integration. A multiple q-integral over an order polytope of a poset is interpreted as a generating function of linear extensions of the poset. Specific modifications of posets are shown to give predictable changes in q-integrals over their respective order polytopes. This method is used to combinatorially evaluate some generalized q-beta integrals. One such application is a combinatorial interpretation of a q-Selberg integral. New generating functions for generalized Gelfand–Tsetlin patterns and reverse plane partitions are established. A q-analogue to a well known result in Ehrhart theory is generalized using q-volumes and q-Ehrhart polynomials.