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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/2509.17541 |
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| _version_ | 1866908552209104896 |
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| author | Freij-Hollanti, Ragnar Lundström, Teemu Mori, Aki |
| author_facet | Freij-Hollanti, Ragnar Lundström, Teemu Mori, Aki |
| contents | We give an explicit combinatorial description of the two-dimensional faces of both the order polytope $\mathcal{O}(P)$ and the chain polytope $\mathcal{C}(P)$ of a partially ordered set $P$. Using these descriptions, we show that for any $P$, $\mathcal{C}(P)$ has equally many square faces, and at least as many triangular faces, as $\mathcal{O}(P)$ does. Moreover, the inequality is shown to be strict except when $\mathcal{O}(P)$ and $\mathcal{C}(P)$ are unimodularly equivalent. This proves the case $i=2$ of a conjecture by Hibi and Li. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-Dimensional Faces of Order and Chain Polytopes Freij-Hollanti, Ragnar Lundström, Teemu Mori, Aki Combinatorics We give an explicit combinatorial description of the two-dimensional faces of both the order polytope $\mathcal{O}(P)$ and the chain polytope $\mathcal{C}(P)$ of a partially ordered set $P$. Using these descriptions, we show that for any $P$, $\mathcal{C}(P)$ has equally many square faces, and at least as many triangular faces, as $\mathcal{O}(P)$ does. Moreover, the inequality is shown to be strict except when $\mathcal{O}(P)$ and $\mathcal{C}(P)$ are unimodularly equivalent. This proves the case $i=2$ of a conjecture by Hibi and Li. |
| title | Two-Dimensional Faces of Order and Chain Polytopes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.17541 |