Unimodality of Eulerian quasisymmetric functions

Abstract

We prove two conjectures of Shareshian and Wachs about Eulerian quasisymmetric functions and polynomials. The first states that the cycle type Eulerian quasisymmetric function $Q_{\lambda ,j}$ is Schur-positive, and moreover that the sequence $Q_{\lambda ,j}$ as $j$ varies is Schur-unimodal. The second conjecture, which we prove using the first, states that the cycle type $(q,p)$-Eulerian polynomial \newline $A_λ^{\maj,\des,\exc}(q,p,q^{-1}t)$ is $t$-unimodal.

15 pages

References in corpus (1)

• Representations of wreath products on cohomology of De Concini-Procesi compactifications

Cited by in corpus (1)

• From Poset Topology to $q$-Eulerian Polynomials to Stanley's Chromatic Symmetric Functions