Higher cosystoles of matroids
Combinatorics
2026-05-21 v1
Abstract
We define a matroid invariant called the three-cosystole that is related to higher notions of cogirth for weighted matroids, and we prove an optimal upper bound for it in the class of regular matroids of rank at most six. To accomplish this, we show that it is increasing under matroid extensions and then estimate it for each of the maximal simple regular matroids of rank at most six.
Keywords
Cite
@article{arxiv.2605.20409,
title = {Higher cosystoles of matroids},
author = {James Dylan Douthitt and Elana Israel and Lee Kennard},
journal= {arXiv preprint arXiv:2605.20409},
year = {2026}
}