Weighted Ehrhart functions

Abstract We give an algorithm for computing weighted Ehrhart functions of lattice polytopes with polynomial weights on its lattice points using Lagrange interpolation. We show how to compute generating functions of polynomials using those of unit cubes and Eulerian numbers, and apply integer programming to study the algebraic properties of the Ehrhart ring of the d -th unit cube. We then present some applications to weighted Ehrhart functions and enumeration problems using linear functions and homogeneous polynomials as weights.