## 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 from Khovanov homology to construct a homology theory of graded S_{n}-modules, whose graded Frobenius series Frob_{G}(q,t) specializes to the chromatic symmetric function at q=t=1. This homology theory can be thought of as a categorification of the chromatic symmetric function, and it satisfies homological analogues of several familiar properties of X_{G}. In particular, the decomposition formula for X_{G} discovered recently by Orellana, Scott, and independently by Guay-Paquet, is lifted to a long exact sequence in homology.

Original language | English |
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Pages (from-to) | 218-246 |

Number of pages | 29 |

Journal | Journal of Combinatorial Theory. Series A |

Volume | 154 |

DOIs | |

State | Published - Feb 2018 |

### Bibliographical note

Publisher Copyright:© 2017 Elsevier Inc.

## Keywords

- Chromatic polynomial
- Frobenius series
- Graph coloring
- Khovanov homology
- Representations
- Symmetric functions

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics