QSym over Sym has a stable basis

Details QSym over Sym has a stable basis QSym over Sym has a stable basis

2010-03-10

arxiv.org/abs/1003.2124v1

Mathematics

Combinatorics

12 pages

Scientific paper

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!.

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