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arXiv · 2604.08394

Ehrhart positivity for marked order polytopes

Katharina Jochemko·Krishna Menon
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Abstract

Given a pair of finite posets $A \subseteq P$, the function counting integer-valued order preserving extensions of an order preserving map $\lambda : A\rightarrow \mathbb{Z}$ from $A$ to $P$ is given by a piecewise polynomial in $\lambda$. We provide a criterion for the nonnegativity of the coefficients of these multivariate polynomials and apply it to show that marked order polytopes of skew shapes are Ehrhart positive in a multivariate sense. This extends recent results of Ferroni-Morales-Panova on order polytopes of skew shapes and proves conjectures on the Ehrhart positivity of skew Gelfand-Tsetlin polytopes and $m$-generalized Pitman-Stanley polytopes due to Alexanderson-Alhajjar and Dugan-Hegarty-Morales-Raymond, respectively.

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Katharina Jochemko, Krishna Menon. 2026-04-09. Ehrhart positivity for marked order polytopes. https://arxiv.org/abs/2604.08394

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