2007/10/23 by Jesús A. De Loera, David C. Haws, Matthias Köppe · 3 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Commutative Algebra and Its Applications #Graphic matroid #Matroid #Matroid partitioning #Oriented matroid #Polynomial #Polynomial and algebraic computation #Polytope #math.CO #msc:05 #msc:52B
paper · pdf · doi:10.1007/s00454-008-9080-z
published as Discrete Comput. Geom. 42 (2009), no. 4, 670-702 · 28 pages, 6 figures, submitted to Discrete and Computational Geometry
arxiv created 2007/10/23 · openalex publication_date 2008/05/08 · openalex created_date 2016/06/24 · arxiv updated 2017/01/03 · openalex updated_date 2026/08/06
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.