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A Sharp Basis-Mass Inequality for Binary Matroids without a Fano Minor
Abstract
Let M be a binary matroid of rank r with no F7-minor, and let BM⋆ denote the maximum of its basis-generating polynomial over nonnegative weights of total mass r. We prove the sharp inequality BM⋆≤ 2r/(r+1), with equality holding if and only if the nonloop simplification of M is M(Kr+1). Binary matroids with no F7-minor also form the largest minor-closed class of matroids on which this inequality holds.
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BibTeX
@misc{zhang2026sharp,
title = {{A Sharp Basis-Mass Inequality for Binary Matroids without a Fano Minor}},
author = {Haozhou Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14370},
eprint = {2610.14370},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14370},
}
RIS
TY - UNPB
TI - A Sharp Basis-Mass Inequality for Binary Matroids without a Fano Minor
AU - Haozhou Zhang
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.14370
UR - https://arxiv.org/abs/2610.14370
AB - Let M be a binary matroid of rank r with no F_7-minor, and let B_M^⋆ denote the maximum of its basis-generating polynomial over nonnegative weights of total mass r. We prove the sharp inequality B_M^⋆≤ 2^r/(r+1), with equality holding if and only if the nonloop simplification of M is M(K_r+1). Binary matroids with no F_7-minor also form the largest minor-closed class of matroids on which this inequality holds.
ER -