QSym over Sym has a stable basis

2010/03/10 by Aaron Lauve, Lauve, Aaron, Sarah Mason +1 · 1 citation
Mathematics · #05E05 #13A50 #16W22 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1003.2124

openalex publication_date 2010/03/10 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We prove that the subset of quasisymmetric polynomials conjectured by Bergeron and Reutenauer to be a basis for the coinvariant space of quasisymmetric polynomials is indeed a basis. This provides the first constructive proof of the Garsia-Wallach result stating that quasisymmetric polynomials form a free module over symmetric polynomials and that the dimension of this module is n!.

Cited by

• Symmetric quasisymmetric Schur-like functions

Related

• Powersum Bases in Quasisymmetric Functions and Quasisymmetric Functions in Non-commuting Variables
• Three Examples of Quasisymmetric Compatible \mathfrakS_n-modules
• Explicit polynomial generators for the ring of quasi-symmetric functions over the integers
• Symmetric functions, noncommutative symmetric functions, and quasisymmetric functions II
• Equivariant quasisymmetry and noncrossing partitions