On q-integrals over order polytopes
On q-integrals over order polytopes
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关于阶多胞形的 q 积分
DOI：
10.1016/j.aim.2017.01.001
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发表时间：
2016
影响因子：
1.7
通讯作者：
D. Stanton
中科院分区：
文献类型：
--
作者：
J. Kim;D. Stanton
发展了多重积分的组合研究。这包括凸多面体的q体积，它取决于q积分的顺序。偏序集的阶多面体上的多重积分被解释为该偏序集的线性扩张的母函数。偏序集的具体修改给出了它们各自的有序多面体上的q积分的可预测的变化。利用该方法对一些广义q-β积分进行了组合求值。一个这样的应用是对AQ-Selberg积分的组合解释。建立了广义Gelfand-Tsetlin模式和反平面划分的新母函数。利用q-体积和q-Ehrhart多项式推广了Ehrhart理论中的一个著名结果。
A combinatorial study of multipleq-integrals is developed. This includes aq-volume of a convex polytope, which depends upon the order ofq-integration. A multipleq-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 inq-integrals over their respective order polytopes. This method is used to combinatorially evaluate some generalizedq-beta integrals. One such application is a combinatorial interpretation of aq-Selberg integral. New generating functions for generalized Gelfand–Tsetlin patterns and reverse plane partitions are established. Aq-analogue to a well known result in Ehrhart theory is generalized usingq-volumes andq-Ehrhart polynomials.