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!.
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