Chromatic quasisymmetric functions

John Shareshian, Michelle L. Wachs

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


We introduce a quasisymmetric refinement of Stanley's chromatic symmetric function. We derive refinements of both Gasharov's Schur-basis expansion of the chromatic symmetric function and Chow's expansion in Gessel's basis of fundamental quasisymmetric functions. We present a conjectural refinement of Stanley's power sum basis expansion, which we prove in special cases. We describe connections between the chromatic quasisymmetric function and both the q-Eulerian polynomials introduced in our earlier work and, conjecturally, representations of symmetric groups on cohomology of regular semisimple Hessenberg varieties, which have been studied by Tymoczko and others. We discuss an approach, using the results and conjectures herein, to the e-positivity conjecture of Stanley and Stembridge for incomparability graphs of (3 + 1)-free posets.

Original languageEnglish (US)
Pages (from-to)497-551
Number of pages55
JournalAdvances in Mathematics
StatePublished - Jun 4 2016


  • E-Positivity
  • Eulerian polynomials
  • Hessenberg varieties
  • Symmetric functions
  • Unimodality

ASJC Scopus subject areas

  • Mathematics(all)


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