Unimodality of Eulerian quasisymmetric functions

Anthony Henderson, Michelle L. Wachs

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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
Volume119
Issue number1
DOIs
StatePublished - Jan 1 2012

Keywords

  • 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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