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arXiv · 2402.09851

A categorification for the characteristic polynomial of matroids

Takuya Saito·So Yamagata
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Abstract

In the present paper, we provide cohomology groups for matroids, 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.

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Takuya Saito, So Yamagata. 2026-06-16. A categorification for the characteristic polynomial of matroids. https://arxiv.org/abs/2402.09851

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