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arXiv · 1506.03133

A categorification of the chromatic symmetric function

Radmila Sazdanovic·Martha Yip
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Abstract

The Stanley chromatic symmetric function $X_G$ of a graph $G$ is a symmetric function generalization of the chromatic polynomial, and has interesting combinatorial properties. We apply the ideas of Khovanov homology to construct a homology of graded $S_n$-modules, whose graded Frobenius series $Frob_G(q,t)$ reduces to the chromatic symmetric function at $q=t=1$. This homology can be thought of as a categorification of the chromatic symmetric function, and provides a homological analogue of several familiar properties of $X_G$. In particular, the decomposition formula for $X_G$ discovered recently by Orellana and Scott, and Guay-Paquet is lifted to a long exact sequence in homology.

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Radmila Sazdanovic, Martha Yip. 2015-06-09. A categorification of the chromatic symmetric function. https://arxiv.org/abs/1506.03133

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