English

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