Free quasi-symmetric functions of arbitrary level

2004/05/31 by Jean-Christophe Novelli, Novelli, Jean-Christophe, Jean‐Yves Thibon +2
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #math.CO

paper · pdf · doi:10.48550/arxiv.math/0405597

11 pages, AMS LaTex

openalex publication_date 2004/05/31 · arxiv created 2004/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce analogues of the Hopf algebra of Free quasi-symmetric functions with bases labelled by colored permutations. As applications, we recover in a simple way the descent algebras associated with wreath products Γ\wr\SG_n and the corresponding generalizations of quasi-symmetric functions. Also, we obtain Hopf algebras of colored parking functions, colored non-crossing partitions and parking functions of type B.

Related

• Symmetric functions, noncommutative symmetric functions, and quasisymmetric functions
• Symmetric functions, noncommutative symmetric functions, and quasisymmetric functions II
• Binary shuffle bases for quasi-symmetric functions
• A Hopf algebra generalization of the symmetric functions in partially commutative variables
• Descent representations and colored quasisymmetric functions