English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Eulerian quasisymmetric functions were introduced by Shareshian and Wachs inorder to obtain a q-analog of Euler's exponential generating function formulafor the Eulerian numbers. They are defined via the symmetric group, andapplying the stable and nonstable principal specializations yields formulas forjoint distributions of permutation statistics. We consider the wreath productof the cyclic group with the symmetric group, also known as the group ofcolored permutations. We use this group to introduce colored Eulerianquasisymmetric functions, which are a generalization of Eulerian quasisymmetricfunctions. We derive a formula for the generating function of these coloredEulerian quasisymmetric functions, which reduces to a formula of Shareshian andWachs for the Eulerian quasisymmetric functions. We show that applying thestable and nonstable principal specializations yields formulas for jointdistributions of colored permutation statistics, which generalize theShareshian-Wachs q-analog of Euler's formula, formulas of Foata and Han, and aformula of Chow and Gessel.

Eulerian quasisymmetric functions for the type B Coxeter group and other wreath product groups