Weighted Ehrhart functions

Abstract

We give an algorithm to compute weighted Ehrhart functions of lattice polytopes for polynomial weights using Lagrange interpolation. We show how to compute generating functions of polynomials using those of unit cubes and Eulerian numbers, and use integer programming to study the algebraic properties of the Ehrhart ring of the $d$-th unit cube. Then we show some applications to weighted Ehrhart functions and enumeration problems.