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arXiv · 2610.03122

Series-parallel extensions and Ehrhart positivity

Yao Li·Sihong Shao
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Abstract

We prove Ehrhart positivity for series-parallel matroids and extend this result to all series-parallel extensions of multi-path matroids. A formula for the Ehrhart coefficients of series-parallel matroids is derived and used to prove strict positivity. An extension criterion based on weighted lattice-point counts is established. Recursive formulas for lattice-point counts are derived, and the recursion is shown to preserve a class of polynomials with nonnegative coefficients. We finally construct a connected transversal matroid with a negative Ehrhart coefficient, disproving the conjecture of Ferroni, Morales, and Panova that every connected matroid whose base polytope admits a subdivision into series-parallel matroid base polytopes is Ehrhart positive.

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Yao Li, Sihong Shao. 2026-10-02. Series-parallel extensions and Ehrhart positivity. https://arxiv.org/abs/2610.03122

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