Unimodality of Eulerian quasisymmetric functions

Anthony Henderson, Michelle L Galloway

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 2012

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Quasi-symmetric Functions
Unimodality
Polynomials
Cycle
Polynomial
Vary

Keywords

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

ASJC Scopus subject areas

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

Cite this

Unimodality of Eulerian quasisymmetric functions. / Henderson, Anthony; Galloway, Michelle L.

In: Journal of Combinatorial Theory, Series A, Vol. 119, No. 1, 01.2012, p. 135-145.

Research output: Contribution to journalArticle

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