The Ehrhart polynomial of a matroid specializes to the β -invariant

Advances in Geometry 2026 Open access

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Authors: Anastasia Chavez, Galen Dorpalen‐Barry, Luis Ferroni, Fu Liu, Felipe Rincón, Andrés R. Vindas-Meléndez
DOI: 10.1515/advgeom-2025-0038
Cited by: 1
References: 31

Abstract

Abstract We show that the linear coefficient of the Ehrhart polynomial of a matroid base polytope evaluated at t − 1 is equal to, up to normalization, the β -invariant of the matroid. This yields a lattice-point counting formula for the β -invariant and establishes a new and unexpected positivity property of Ehrhart polynomials of matroid polytopes.

Fields of Study & Subjects

Advanced Combinatorial Mathematics Polynomial and algebraic computation Commutative Algebra and Its Applications

Publication details

Journal / source
Advances in Geometry
Publisher
Walter de Gruyter GmbH
Volume
26
Issue
1
Pages
127–133
Publication date
1 January 2026
Language
EN