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arXiv · 2608.28585

The Tutte polynomial determines the linear coefficient of the Ehrhart polynomial

Erik Panzer
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Abstract

We prove a formula for the linear coefficient of the Ehrhart polynomial in terms of the Tutte polynomial. Furthermore, we characterize the matroids that extremize this Ehrhart coefficient, proving a conjecture of Ferroni.

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Erik Panzer. 2026-08-28. The Tutte polynomial determines the linear coefficient of the Ehrhart polynomial. https://arxiv.org/abs/2608.28585

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