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arXiv:2402.09851 [math.CO]AbstractReferencesReviewsResources

A categorification for the characteristic polynomial of matroids

Takuya Saito, So Yamagata

Published 2024-02-15, updated 2024-09-04Version 2

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.

Comments: 25 pages, 2 figures
Categories: math.CO, math.AT, math.GT
Subjects: 05B35, 05C15, 05C31, 57K18
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