A genetic algorithm to search the space of Ehrhart $h^*$-vectors
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912083782664192 |
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| author | Balletti, Gabriele |
| author_facet | Balletti, Gabriele |
| contents | We describe a genetic algorithm to find candidates for $h^*$-vectors satisfying given properties in the space of integers vectors of finite length. We use an implementation of such algorithm to find a 52-dimensional lattice polytope having a non-unimodal $h^*$-vector which is the Cartesian product of two lattice polytopes having unimodal $h^*$-vectors. This counterexample answers negatively to a question by Ferroni and Higashitani. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16848 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A genetic algorithm to search the space of Ehrhart $h^*$-vectors Balletti, Gabriele Combinatorics Commutative Algebra Optimization and Control 52B20 (Primary) 05A20, 68W50 (Secondary) We describe a genetic algorithm to find candidates for $h^*$-vectors satisfying given properties in the space of integers vectors of finite length. We use an implementation of such algorithm to find a 52-dimensional lattice polytope having a non-unimodal $h^*$-vector which is the Cartesian product of two lattice polytopes having unimodal $h^*$-vectors. This counterexample answers negatively to a question by Ferroni and Higashitani. |
| title | A genetic algorithm to search the space of Ehrhart $h^*$-vectors |
| topic | Combinatorics Commutative Algebra Optimization and Control 52B20 (Primary) 05A20, 68W50 (Secondary) |
| url | https://arxiv.org/abs/2309.16848 |