Computing parametric weighted Ehrhart polynomials of smooth polytopes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911262420500480 |
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| author | Hwang, Daniel Whidden, Juliet Yu, Josephine |
| author_facet | Hwang, Daniel Whidden, Juliet Yu, Josephine |
| contents | We show that when integral polytopes are deformed while keeping the same facet normal vectors, the coefficients of weighted Ehrhart and $h^*$-polynomials are piecewise polynomial functions in the ``right hand sides'' of the linear inequalities defining the polytopes. We give an algorithm and an implementation in SageMath for computing these polynomials for smooth polytopes, such as type $A$ alcoved polytopes, using a weighted Euler-Maclaurin type formula by Khovanskiǐ and Pukhlikov. We discuss some natural questions concerning signs of the coefficients of the weighted $h^*$-polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09744 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing parametric weighted Ehrhart polynomials of smooth polytopes Hwang, Daniel Whidden, Juliet Yu, Josephine Combinatorics 52B20 We show that when integral polytopes are deformed while keeping the same facet normal vectors, the coefficients of weighted Ehrhart and $h^*$-polynomials are piecewise polynomial functions in the ``right hand sides'' of the linear inequalities defining the polytopes. We give an algorithm and an implementation in SageMath for computing these polynomials for smooth polytopes, such as type $A$ alcoved polytopes, using a weighted Euler-Maclaurin type formula by Khovanskiǐ and Pukhlikov. We discuss some natural questions concerning signs of the coefficients of the weighted $h^*$-polynomials. |
| title | Computing parametric weighted Ehrhart polynomials of smooth polytopes |
| topic | Combinatorics 52B20 |
| url | https://arxiv.org/abs/2511.09744 |