Ehrhart polynomials of matroid polytopes and polymatroids

Details Ehrhart polynomials of matroid polytopes and polymatroids Ehrhart polynomials of matroid polytopes and polymatroids

2007-10-23

arxiv.org/abs/0710.4346v1

Mathematics

Combinatorics

28 pages, 6 figures, submitted to Discrete and Computational Geometry

Scientific paper

We investigate properties of Ehrhart polynomials for matroid polytopes, independence matroid polytopes, and polymatroids. In the first half of the paper we prove that for fixed rank their Ehrhart polynomials are computable in polynomial time. The proof relies on the geometry of these polytopes as well as a new refined analysis of the evaluation of Todd polynomials. In the second half we discuss two conjectures about the h^*-vector and the coefficients of Ehrhart polynomials of matroid polytopes; we provide theoretical and computational evidence for their validity.

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