Ehrhart Polynomials of Matroid Polytopes and Polymatroids

被引：15

作者：

De Loera, Jesus A. ^{[1
]}

Haws, David C. ^{[1
]}

Koeppe, Matthias ^{[2
]}

机构：

[1] Univ Calif Davis, Dept Math, Davis, CA 95616 USA

[2] Otto VonGuericke Univ Magdegurg, Dept Math, IMO, D-39106 Magdeburg, Germany

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2009年 / 42卷 / 04期

关键词：

Matroid; Matroid polytopes; Polymatroids; Ehrhart polynomials; Volume computation; Rational generating functions; h*-vector; Unimodality; Ehrhart series; RATIONAL GENERATING-FUNCTIONS; PRIMAL BARVINOK ALGORITHM; VOLUME COMPUTATION; CONVEX-POLYHEDRA; INTEGRAL-POINTS; VERONESE TYPE; COMPLEXITY; ALGEBRAS;

D O I：

10.1007/s00454-008-9080-z

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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, Ehrhart polynomials of matroid polytopes and polymatroids 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.

引用

页码：670 / 702

页数：33

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