# Computation of the Highest Coefficients of Weighted Ehrhart Quasi-polynomials of Rational Polyhedra

@article{Baldoni2012ComputationOT,
title={Computation of the Highest Coefficients of Weighted Ehrhart Quasi-polynomials of Rational Polyhedra},
author={Velleda Baldoni and Nicole Berline and Jes{\'u}s A. De Loera and Matthias K{\"o}ppe and Mich{\e}le Vergne},
journal={Foundations of Computational Mathematics},
year={2012},
volume={12},
pages={435-469}
}`
• Published 6 November 2010
• Mathematics
• Foundations of Computational Mathematics
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 in the…
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