PreprintCC BY 4.0arXiv
The Tutte polynomial determines the linear coefficient of the Ehrhart polynomial
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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BibTeX
@misc{panzer2026tutte,
title = {{The Tutte polynomial determines the linear coefficient of the Ehrhart polynomial}},
author = {Erik Panzer},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28585},
eprint = {2608.28585},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28585},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Tutte polynomial determines the linear coefficient of the Ehrhart polynomial
AU - Erik Panzer
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28585
UR - https://arxiv.org/abs/2608.28585
AB - 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.
ER -