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arXiv · 2604.27515

Vertex Posets, Monotone Path Polytopes, and Chow Polynomials

Mateusz Michałek·Leonid Monin·Botong Wang
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Abstract

Let $P\subset\mathbb R^n$ be a convex polytope and let $\ell$ be a linear functional which is nonconstant on every edge of $P$. The induced acyclic orientation determines positive and negative Bia{\l}ynicki-Birula type partitions of $P$ into unions of relative interiors of faces. Our first result establishes a duality: the positive partition is a stratification if and only if the negative one is a stratification. Our second result connects poset invariants with monotone path polytopes. Assuming the induced vertex relation admits the structure of a graded poset, we prove that the Chow polynomial of the resulting vertex poset agrees with the $h$-polynomial of a (dual) monotone path polytope.

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Mateusz Michałek, Leonid Monin, Botong Wang. 2026-04-30. Vertex Posets, Monotone Path Polytopes, and Chow Polynomials. https://arxiv.org/abs/2604.27515

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