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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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Table of 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.