English

QSym over Sym has a stable basis

Combinatorics 2010-03-11 v1

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!.

Keywords

Cite

@article{arxiv.1003.2124,
  title  = {QSym over Sym has a stable basis},
  author = {Aaron Lauve and Sarah Mason},
  journal= {arXiv preprint arXiv:1003.2124},
  year   = {2010}
}

Comments

12 pages

R2 v1 2026-06-21T14:56:09.507Z