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arXiv · 2607.00922

Order polytopes of generalized snake posets are $h^*$-real-rooted

Benjamin Braun·Aryaman Jal
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Abstract

Order polytopes for generalized snake posets were recently studied by von Bell et al. (2022), and are known to be unimodularly equivalent to strength-one flow polytopes for acyclic directed graphs strongly dual to generalized snake posets. Lee, Vindas-Mel\'endez, and Wang (2026) conjectured that the Ehrhart $h^*$-polynomials of these order polytopes are real-rooted. We prove this conjecture using a connection between these $h^*$-polynomials and non-nesting rook polynomials, which were recently introduced by Alexandersson and Jal (2024+) in connection with $P$-Eulerian polynomials for width two posets.

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Benjamin Braun, Aryaman Jal. 2026-07-01. Order polytopes of generalized snake posets are $h^*$-real-rooted. https://arxiv.org/abs/2607.00922

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