Thin Simplices via Modular Arithmetic
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911330209890304 |
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| author | Kurylenko, Vadym |
| author_facet | Kurylenko, Vadym |
| contents | The local $h^*$-polynomial is a natural invariant of a lattice polytope appearing in Ehrhart theory and Hodge theory. In this work, we study the question posed in [GKZ94] concerning the classification of lattice simplices with vanishing local $h^*$-polynomial. Such simplices are called thin. We relate this question to linear codes and hyperplane arrangements over finite rings. This allows us to obtain a complete classification of the $4$-dimensional thin simplices, extending the previously known results in dimensions up to $3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thin Simplices via Modular Arithmetic Kurylenko, Vadym Combinatorics Algebraic Geometry 52B20 (Primary) 94B05, 52C35 (Secondary) The local $h^*$-polynomial is a natural invariant of a lattice polytope appearing in Ehrhart theory and Hodge theory. In this work, we study the question posed in [GKZ94] concerning the classification of lattice simplices with vanishing local $h^*$-polynomial. Such simplices are called thin. We relate this question to linear codes and hyperplane arrangements over finite rings. This allows us to obtain a complete classification of the $4$-dimensional thin simplices, extending the previously known results in dimensions up to $3$. |
| title | Thin Simplices via Modular Arithmetic |
| topic | Combinatorics Algebraic Geometry 52B20 (Primary) 94B05, 52C35 (Secondary) |
| url | https://arxiv.org/abs/2404.03975 |