Unimodality of Eulerian quasisymmetric functions

Authors:
Anthony Henderson;Michelle L. Wachs
Affiliations:
School of Mathematics and Statistics, University of Sydney NSW 2006, Australia;Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA
Venue:
Journal of Combinatorial Theory Series A
Year:
2012

Citing 3
Cited 0

Eulerian numbers, tableaux, and the Betti numbers of a toric variety

Discrete Mathematics - Special volume: algebraic combinatorics
Counting permutations with given cycle structure and descent set

Journal of Combinatorial Theory Series A
Whitney Homology of Semipure Shellable Posets

Journal of Algebraic Combinatorics: An International Journal

Quantified Score

Hi-index	0.00

Visualization

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 Q"@l","j is Schur-positive, and moreover that the sequence Q"@l","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 A"@l^m^a^j^,^d^e^s^,^e^x^c(q,p,q^-^1t) is t-unimodal.