# 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} }

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…

## 31 Citations

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- MathematicsArXiv
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