On q-integrals over order polytopes
arXiv:1608.03342
Abstract
A combinatorial study of multiple -integrals is developed. This includes a -volume of a convex polytope, which depends upon the order of -integration. A multiple -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 -integrals over their respective order polytopes. This method is used to combinatorially evaluate some generalized -beta integrals. One such application is a combinatorial interpretation of a -Selberg integral. New generating functions for generalized Gelfand-Tsetlin patterns and reverse plane partitions are established. A -analogue to a well known result in Ehrhart theory is generalized using -volumes and -Ehrhart polynomials.
33 pages, 8 figures