Ehrhart non-positivity and unimodular triangulations for classes of s-lecture hall simplices
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915686687703040 |
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| author | Caicedo, Jhon B. Juhnke, Martina Poullot, Germain |
| author_facet | Caicedo, Jhon B. Juhnke, Martina Poullot, Germain |
| contents | Counting lattice points and triangulating polytopes is a prominent subject in discrete geometry, yet proving Ehrhart positivity or existence of unimodular triangulations remain of utmost difficulty in general, even for ``easy'' simplices. We study these questions for classes of s-lecture hall simplices. Inspired by a question of Olsen, we present a new natural class of sequences s for which the s-lecture hall simplices are not Ehrhart positive, by explicitly estimating a negative coefficient. Meanwhile, motivated by a conjecture of Hibi, Olsen and Tsuchiya, we extend the previously known classes of sequences s for which the s-lecture hall simplex admits a flag, regular and unimodular triangulation. The triangulations we construct are explicit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_18890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ehrhart non-positivity and unimodular triangulations for classes of s-lecture hall simplices Caicedo, Jhon B. Juhnke, Martina Poullot, Germain Combinatorics 52B20, 52B05, 52B11 Counting lattice points and triangulating polytopes is a prominent subject in discrete geometry, yet proving Ehrhart positivity or existence of unimodular triangulations remain of utmost difficulty in general, even for ``easy'' simplices. We study these questions for classes of s-lecture hall simplices. Inspired by a question of Olsen, we present a new natural class of sequences s for which the s-lecture hall simplices are not Ehrhart positive, by explicitly estimating a negative coefficient. Meanwhile, motivated by a conjecture of Hibi, Olsen and Tsuchiya, we extend the previously known classes of sequences s for which the s-lecture hall simplex admits a flag, regular and unimodular triangulation. The triangulations we construct are explicit. |
| title | Ehrhart non-positivity and unimodular triangulations for classes of s-lecture hall simplices |
| topic | Combinatorics 52B20, 52B05, 52B11 |
| url | https://arxiv.org/abs/2508.18890 |