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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2601.22992 |
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| _version_ | 1866908807393705984 |
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| author | McAllister, Tyrrell B. Rochais, Hélène O. |
| author_facet | McAllister, Tyrrell B. Rochais, Hélène O. |
| contents | Let $\mathcal{P} \subseteq \mathbb{R}^{n}$ be a polytope whose vertices have rational coordinates. By a seminal result of E. Ehrhart, the number of integer lattice points in the $k$th dilate of $\mathcal{P}$ ($k$ a positive integer) is a quasi-polynomial function of $k$ -- that is, a "polynomial" in which the coefficients are themselves periodic functions of $k$. It is an open problem to determine which quasi-polynomials are the Ehrhart quasi-polynomials of rational polytopes. As partial progress on this problem, we construct families of polytopes in which the periods of the coefficient functions take on various prescribed values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22992 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Periods of Ehrhart coefficients of rational polytopes McAllister, Tyrrell B. Rochais, Hélène O. Combinatorics Let $\mathcal{P} \subseteq \mathbb{R}^{n}$ be a polytope whose vertices have rational coordinates. By a seminal result of E. Ehrhart, the number of integer lattice points in the $k$th dilate of $\mathcal{P}$ ($k$ a positive integer) is a quasi-polynomial function of $k$ -- that is, a "polynomial" in which the coefficients are themselves periodic functions of $k$. It is an open problem to determine which quasi-polynomials are the Ehrhart quasi-polynomials of rational polytopes. As partial progress on this problem, we construct families of polytopes in which the periods of the coefficient functions take on various prescribed values. |
| title | Periods of Ehrhart coefficients of rational polytopes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.22992 |