Unimodality of Eulerian quasisymmetric functions

Anthony Henderson, Michelle L. Wachs

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We prove two conjectures of Shareshian and Wachs about Eulerian quasisymmetric functions and Eulerian polynomials. The first states that the cycle type Eulerian quasisymmetric function Qλ,j is Schur-positive, and moreover that the sequence Qλ,j as j varies is Schur-unimodal. The second conjecture, which we prove using the first, states that the cycle type (q, p)-Eulerian polynomial Aλmaj,des,exc(q,p,q-1t) is t-unimodal.

Original languageEnglish (US)
Pages (from-to)135-145
Number of pages11
JournalJournal of Combinatorial Theory. Series A
Issue number1
StatePublished - Jan 2012


  • Cycle type
  • Eulerian polynomials
  • Permutation statistics
  • Symmetric functions
  • Unimodality

ASJC Scopus subject areas

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


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