The Stanley chromatic symmetric function XG 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 Sn-modules, whose graded Frobenius series FrobG(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 XG. In particular, the decomposition formula for XG discovered recently by Orellana, Scott, and independently by Guay-Paquet, is lifted to a long exact sequence in homology.
|Number of pages||29|
|Journal||Journal of Combinatorial Theory. Series A|
|State||Published - Feb 2018|
Bibliographical notePublisher Copyright:
© 2017 Elsevier Inc.
- Chromatic polynomial
- Frobenius series
- Graph coloring
- Khovanov homology
- Symmetric functions
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics