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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.01743 |
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| _version_ | 1866910788465197056 |
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| author | Jiang, Yuhan |
| author_facet | Jiang, Yuhan |
| contents | A positroid is a matroid realized by a matrix such that all maximal minors are non-negative. Positroid polytopes are matroid polytopes of positroids. In particular, they are lattice polytopes. The Ehrhart polynomial of a lattice polytope counts the number of integer points in the dilation of that polytope. The Ehrhart series is the generating function of the Ehrhart polynomial, a rational function with a numerator called the $h^*$-polynomial. We give explicit formulas for the $h^*$-polynomials of an arbitrary positroid polytope regarding permutation descents. Our result generalizes that of Early, Kim, and Li for hypersimplices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01743 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Ehrhart $h^*$-polynomials of positroid polytopes Jiang, Yuhan Combinatorics A positroid is a matroid realized by a matrix such that all maximal minors are non-negative. Positroid polytopes are matroid polytopes of positroids. In particular, they are lattice polytopes. The Ehrhart polynomial of a lattice polytope counts the number of integer points in the dilation of that polytope. The Ehrhart series is the generating function of the Ehrhart polynomial, a rational function with a numerator called the $h^*$-polynomial. We give explicit formulas for the $h^*$-polynomials of an arbitrary positroid polytope regarding permutation descents. Our result generalizes that of Early, Kim, and Li for hypersimplices. |
| title | The Ehrhart $h^*$-polynomials of positroid polytopes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.01743 |