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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2309.01186 |
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| _version_ | 1866916548844716032 |
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| author | Bajo, Esme Braun, Benjamin Codenotti, Giulia Hofscheier, Johannes Vindas-Meléndez, Andrés R. |
| author_facet | Bajo, Esme Braun, Benjamin Codenotti, Giulia Hofscheier, Johannes Vindas-Meléndez, Andrés R. |
| contents | The local $h^*$-polynomial of a lattice polytope is an important invariant arising in Ehrhart theory. Our focus is on lattice simplices presented in Hermite normal form with a single non-trivial row. We prove that when the off-diagonal entries are fixed, the distribution of coefficients for the local $h^*$-polynomial of these simplices has a limit as the normalized volume goes to infinity. Further, this limiting distribution is determined by the coefficients for a particular choice of normalized volume. We also provide an analysis of two specific families of such simplices to illustrate and motivate our main result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01186 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local $h^*$-polynomials for one-row Hermite normal form simplices Bajo, Esme Braun, Benjamin Codenotti, Giulia Hofscheier, Johannes Vindas-Meléndez, Andrés R. Combinatorics The local $h^*$-polynomial of a lattice polytope is an important invariant arising in Ehrhart theory. Our focus is on lattice simplices presented in Hermite normal form with a single non-trivial row. We prove that when the off-diagonal entries are fixed, the distribution of coefficients for the local $h^*$-polynomial of these simplices has a limit as the normalized volume goes to infinity. Further, this limiting distribution is determined by the coefficients for a particular choice of normalized volume. We also provide an analysis of two specific families of such simplices to illustrate and motivate our main result. |
| title | Local $h^*$-polynomials for one-row Hermite normal form simplices |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2309.01186 |