Order and chain polytopes of maximal ranked posets
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915934060412928 |
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| author | Ahmad, Ibrahim Fourier, Ghislain Joswig, Michael |
| author_facet | Ahmad, Ibrahim Fourier, Ghislain Joswig, Michael |
| contents | The order and chain polytopes, introduced by Richard P. Stanley, form a pair of Ehrhart equivalent polytopes associated to a given finite poset. A conjecture by Takayuki Hibi and Nan Li states that the $f$-vector of the chain polytope dominates the $f$-vector of the order polytope. In this paper we prove a stronger form of that conjecture for a special class of posets. More precisely, we show that the $f$-vectors increase monotonically over an admissible family of chain-order polytopes for such posets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01626 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Order and chain polytopes of maximal ranked posets Ahmad, Ibrahim Fourier, Ghislain Joswig, Michael Combinatorics 52B05, 52B20 The order and chain polytopes, introduced by Richard P. Stanley, form a pair of Ehrhart equivalent polytopes associated to a given finite poset. A conjecture by Takayuki Hibi and Nan Li states that the $f$-vector of the chain polytope dominates the $f$-vector of the order polytope. In this paper we prove a stronger form of that conjecture for a special class of posets. More precisely, we show that the $f$-vectors increase monotonically over an admissible family of chain-order polytopes for such posets. |
| title | Order and chain polytopes of maximal ranked posets |
| topic | Combinatorics 52B05, 52B20 |
| url | https://arxiv.org/abs/2309.01626 |