A categorification of the chromatic symmetric polynomial

Radmila Sazdanović, Martha Yip

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


The Stanley chromatic symmetric polynomial of a graph G is a symmetric function generalization of the chromatic polynomial, and has interesting combinatorial properties. We apply the techniques of Khovanov homology to construct a homology H∗(G) of graded Sn-modules, whose bigraded Frobenius series FrobG(q, t) reduces to the chromatic symmetric polynomial at q = t = 1. We also obtain analogues of several familiar properties of the chromatic symmetric polynomials in terms of homology.

Original languageEnglish
Pages (from-to)631-642
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2015
Event27th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2015 - Daejeon, Korea, Republic of
Duration: Jul 6 2015Jul 10 2015

Bibliographical note

Funding Information:
The former author would like to thank the Simons Foundation for its support via the AMS Travel and Simons Collaboration grants. The latter author would like to thank Chris Hays for helpful suggestions.

Publisher Copyright:
© 2015 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France


  • Chromatic polynomial
  • Frobenius series
  • Graph colouring
  • Khovanov homology
  • Sn-modules
  • Symmetric functions

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)
  • Discrete Mathematics and Combinatorics


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