The Ehrhart polynomial of a matroid specializes to the <i>β</i> -invariant
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.
Authors
- Anastasia Chavez (ORCID: https://orcid.org/0000-0003-2298-930X)
- Luis Ferroni (ORCID: https://orcid.org/0000-0001-5181-7932)
- Andrés R. Vindas-Meléndez (ORCID: https://orcid.org/0000-0002-7437-3745)
- Galen Dorpalen‐Barry (ORCID: https://orcid.org/0000-0002-4951-4913)
- Fu Liu
- Felipe Rincón
Institutions
- University of Pisa (IT)
- Harvey Mudd College (US)
- Queen Mary University of London (GB)
- Saint Mary's College of California (US)
- University of California, Davis (US)
- Texas A&M University (US)
Publication Details
- Journal
- Advances in Geometry
- Published
- 2026-01-01
- DOI
- https://doi.org/10.1515/advgeom-2025-0038
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 0.00