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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2412.02787 |
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| _version_ | 1866915252810022912 |
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| author | Bullock, Elisabeth Jiang, Yuhan |
| author_facet | Bullock, Elisabeth Jiang, Yuhan |
| contents | Alcoved polytopes are convex polytopes, which are the closure of a union of alcoves in an affine Coxeter arrangement. They are rational polytopes and, therefore, have Ehrhart quasipolynomials. Here we describe a method for computing the generating function of the Ehrhart quasipolynomial, or Ehrhart series, of any alcoved polytope via a particular shelling order of its alcoves. We also show a connection between Early's decorated ordered set partitions and this shelling order for the hypersimplex $Δ_{2,n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02787 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Ehrhart series of alcoved polytopes Bullock, Elisabeth Jiang, Yuhan Combinatorics Alcoved polytopes are convex polytopes, which are the closure of a union of alcoves in an affine Coxeter arrangement. They are rational polytopes and, therefore, have Ehrhart quasipolynomials. Here we describe a method for computing the generating function of the Ehrhart quasipolynomial, or Ehrhart series, of any alcoved polytope via a particular shelling order of its alcoves. We also show a connection between Early's decorated ordered set partitions and this shelling order for the hypersimplex $Δ_{2,n}$. |
| title | The Ehrhart series of alcoved polytopes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.02787 |