Ehrhart polynomials of matroid polytopes and polymatroids

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 we...

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Bibliographic Details
Published in:arXiv.org 2007-10
Main Authors: De Loera, Jesús A, Haws, David C, Köppe, Matthias
Format: Article
Language:English
Subjects:
Polynomials
Polytopes
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0710.4346