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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.22981 |
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| _version_ | 1866912735202115584 |
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| author | Mori, Aki Mori, Kenta Ohsugi, Hidefumi |
| author_facet | Mori, Aki Mori, Kenta Ohsugi, Hidefumi |
| contents | Twinned chain polytopes form a broad class of non-centrally symmetric reflexive polytopes and exhibit intriguing structures. In the present paper, we show that the number of facets of $d$-dimensional twinned chain polytopes is at most $6^{d/2}$. In case $d$ is even, the equality holds if and only if the polytope is isomorphic to a free sum of $d/2$ copies of del Pezzo polygons. This result contributes a partial answer to Nill's conjecture: the number of facets of a $d$-dimensional reflexive polytope is at most $6^{d/2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Facet numbers of non-centrally symmetric reflexive polytopes arising from posets Mori, Aki Mori, Kenta Ohsugi, Hidefumi Combinatorics 52B20, 52B12 Twinned chain polytopes form a broad class of non-centrally symmetric reflexive polytopes and exhibit intriguing structures. In the present paper, we show that the number of facets of $d$-dimensional twinned chain polytopes is at most $6^{d/2}$. In case $d$ is even, the equality holds if and only if the polytope is isomorphic to a free sum of $d/2$ copies of del Pezzo polygons. This result contributes a partial answer to Nill's conjecture: the number of facets of a $d$-dimensional reflexive polytope is at most $6^{d/2}$. |
| title | Facet numbers of non-centrally symmetric reflexive polytopes arising from posets |
| topic | Combinatorics 52B20, 52B12 |
| url | https://arxiv.org/abs/2511.22981 |