A categorification of the chromatic symmetric function

Radmila Sazdanovic, Martha Yip

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.

Original languageEnglish
Pages (from-to)218-246
Number of pages29
JournalJournal of Combinatorial Theory. Series A
StatePublished - Feb 2018

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.


  • 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


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