Work

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

Year: 2026

Type: article

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.

Source: Advances in Geometry

DOI: 10.1515/advgeom-2025-0038

Authors: Anastasia Chavez, Galen Dorpalen-Barry, Luis Ferroni, Fu Liu, Felipe Rincón, Andrés R. Vindas-Meléndez

Institutions: Saint Mary's College of California, Texas A&M University, University of Pisa, University of California, Davis, Queen Mary University of London, Harvey Mudd College

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

OpenAlex ID: W7120181641

FWCI: 18.12

Cites: 31

Cited by: 1

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