## Sazdanović, Radmila and Yip, Martha - A categorification of the chromatic symmetric polynomial

dmtcs:2527 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
A categorification of the chromatic symmetric polynomial

Authors: Sazdanović, Radmila and Yip, Martha

The Stanley chromatic polynomial 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 $H$<sub>*</sub>($G$) of graded $S_n$-modules, whose graded Frobenius series $Frob_G(q,t)$ reduces to the chromatic symmetric function at $q=t=1$. We also obtain analogues of several familiar properties of the chromatic symmetric polynomials in terms of homology.

Source : oai:HAL:hal-01337787v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: symmetric functions,chromatic polynomial,Khovanov homology,$S_n$-modules,Frobenius series,graph colouring,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]