Triangular faces of the order and chain polytope of a maximal ranked poset
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929758777901056 |
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| author | Mori, Aki |
| author_facet | Mori, Aki |
| contents | Let $\mathscr{O}(P)$ and $\mathscr{C}(P)$ denote the order polytope and chain polytope, respectively, associated with a finite poset $P$. We prove the following result: if $P$ is a maximal ranked poset, then the number of triangular $2$-faces of $\mathscr{O}(P)$ is less than or equal to that of $\mathscr{C}(P)$, with equality holding if and only if $P$ does not contain an $X$-poset as a subposet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00263 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Triangular faces of the order and chain polytope of a maximal ranked poset Mori, Aki Combinatorics 52B05, 06A07 Let $\mathscr{O}(P)$ and $\mathscr{C}(P)$ denote the order polytope and chain polytope, respectively, associated with a finite poset $P$. We prove the following result: if $P$ is a maximal ranked poset, then the number of triangular $2$-faces of $\mathscr{O}(P)$ is less than or equal to that of $\mathscr{C}(P)$, with equality holding if and only if $P$ does not contain an $X$-poset as a subposet. |
| title | Triangular faces of the order and chain polytope of a maximal ranked poset |
| topic | Combinatorics 52B05, 06A07 |
| url | https://arxiv.org/abs/2404.00263 |