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arXiv · 2605.22673

Ehrhart positivity for lattice path matroids

Luis Ferroni·Alejandro H. Morales·Greta Panova
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Abstract

We prove that all lattice path matroids are Ehrhart positive. This unifies and generalizes numerous results on the Ehrhart positivity of matroids developed over the last two decades. We rely on our previous work on the positivity of order polynomials of fences. Our main result supports the conjecture by Ferroni, Jochemko, and Schr\"oter (2022) on the Ehrhart positivity of positroids. Furthermore, our main result implies that all Schubert matroids are Ehrhart positive, which thus settles a conjecture by Fan and Li (2024), and shows Newton polytopes of certain Schubert and key polynomials are Ehrhart positive.

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Luis Ferroni, Alejandro H. Morales, Greta Panova. 2026-05-21. Ehrhart positivity for lattice path matroids. https://arxiv.org/abs/2605.22673

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