Computation of the highest coefficients of weighted Ehrhart quasi-polynomials of rational polyhedra

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This article concerns the computational problem of counting the lattice points inside convex polytopes, when each point must be counted with a weight associated to it.

• We describe an efficient algorithm for computing the highest degree coefficients of the weighted Ehrhart quasi-polynomial for a rational simple polytope in varying dimension, when the weights of the lattice points are given by a polynomial function h.
• Our technique is based on a refinement of an algorithm of A.
• Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math.