Ehrhart positivity for lattice path matroids
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917520440557568 |
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| author | Ferroni, Luis Morales, Alejandro H. Panova, Greta |
| author_facet | Ferroni, Luis Morales, Alejandro H. Panova, Greta |
| contents | We prove that all lattice path matroids are Ehrhart positive. This unifies and generalizes numerous results on the Ehrhart positivity of matroids developed over the last two decades. We rely on our previous work on the positivity of order polynomials of fences. Our main result supports the conjecture by Ferroni, Jochemko, and Schröter (2022) on the Ehrhart positivity of positroids. Furthermore, our main result implies that all Schubert matroids are Ehrhart positive, which thus settles a conjecture by Fan and Li (2024), and supports a conjecture by Monical, Tokcan, and Yong (2019) on the Ehrhart positivity of Schubitopes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22673 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ehrhart positivity for lattice path matroids Ferroni, Luis Morales, Alejandro H. Panova, Greta Combinatorics We prove that all lattice path matroids are Ehrhart positive. This unifies and generalizes numerous results on the Ehrhart positivity of matroids developed over the last two decades. We rely on our previous work on the positivity of order polynomials of fences. Our main result supports the conjecture by Ferroni, Jochemko, and Schröter (2022) on the Ehrhart positivity of positroids. Furthermore, our main result implies that all Schubert matroids are Ehrhart positive, which thus settles a conjecture by Fan and Li (2024), and supports a conjecture by Monical, Tokcan, and Yong (2019) on the Ehrhart positivity of Schubitopes. |
| title | Ehrhart positivity for lattice path matroids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.22673 |