The Ehrhart polynomial of a matroid specializes to the beta invariant
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866915572866875392 |
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| author | Chavez, Anastasia Dorpalen-Barry, Galen Ferroni, Luis Liu, Fu Rincón, Felipe Vindas-Meléndez, Andrés R. |
| author_facet | Chavez, Anastasia Dorpalen-Barry, Galen Ferroni, Luis Liu, Fu Rincón, Felipe Vindas-Meléndez, Andrés R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Ehrhart polynomial of a matroid specializes to the beta invariant Chavez, Anastasia Dorpalen-Barry, Galen Ferroni, Luis Liu, Fu Rincón, Felipe Vindas-Meléndez, Andrés R. Combinatorics 05B35, 05A15, 52B05, 52B20, 52B40, 05A10 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. |
| title | The Ehrhart polynomial of a matroid specializes to the beta invariant |
| topic | Combinatorics 05B35, 05A15, 52B05, 52B20, 52B40, 05A10 |
| url | https://arxiv.org/abs/2504.15518 |