English

Ehrhart polynomials of matroid polytopes and polymatroids

Combinatorics 2017-01-03 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0710.4346,
  title  = {Ehrhart polynomials of matroid polytopes and polymatroids},
  author = {Jesús A. De Loera and David C. Haws and Matthias Köppe},
  journal= {arXiv preprint arXiv:0710.4346},
  year   = {2017}
}

Comments

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

R2 v1 2026-06-21T09:35:15.719Z