A categorification for the characteristic polynomial of matroids
Combinatorics
2024-09-05 v2 Algebraic Topology
Geometric Topology
Abstract
In the present paper, we provide a cohomology group as a categorification of the characteristic polynomial of matroids. The construction depends on the ``quasi-representation'' of a matroid. For a certain choice of the quasi-representation, we show that our cohomology theory gives a generalization of the chromatic cohomology introduced by L. Helme-Guizon and Y. Rong, and also the characteristic cohomology introduced by Z. Dancso and A. Licata.
Keywords
Cite
@article{arxiv.2402.09851,
title = {A categorification for the characteristic polynomial of matroids},
author = {Takuya Saito and So Yamagata},
journal= {arXiv preprint arXiv:2402.09851},
year = {2024}
}
Comments
25 pages, 2 figures