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arXiv · 2511.03557

Simplex inequalities of order and chain polytopes of recursively defined posets

Ragnar Freij-Hollanti·Teemu Lundström
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Abstract

In this paper, we study the simplex faces of the order polytope $\mathcal{O}(P)$ and the chain polytope $\mathcal{C}(P)$ of a finite poset $P$. We show that, if $P$ can be recursively constructed from $\mathbf{X}$-free posets using disjoint unions and ordinal sums, then $\mathcal{C}(P)$ has at least as many $k$-dimensional simplex faces as $\mathcal{O}(P)$ does, for each dimension $k$. This generalizes a previous result of Mori, both in terms of the dimensions of the simplices and in terms of the class of posets considered.

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Ragnar Freij-Hollanti, Teemu Lundström. 2025-11-05. Simplex inequalities of order and chain polytopes of recursively defined posets. https://arxiv.org/abs/2511.03557

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