The Ehrhart polynomial of a matroid specializes to the beta invariant
Combinatorics
2025-10-27 v2
Abstract
We show that the linear coefficient of the Ehrhart polynomial of a matroid base polytope evaluated at is equal to, up to normalization, the -invariant of the matroid. This yields a lattice-point counting formula for the -invariant and establishes a new and unexpected positivity property of Ehrhart polynomials of matroid polytopes.
Cite
@article{arxiv.2504.15518,
title = {The Ehrhart polynomial of a matroid specializes to the beta invariant},
author = {Anastasia Chavez and Galen Dorpalen-Barry and Luis Ferroni and Fu Liu and Felipe Rincón and Andrés R. Vindas-Meléndez},
journal= {arXiv preprint arXiv:2504.15518},
year = {2025}
}
Comments
v2: version to appear in Advances in Geometry; 8 pages