Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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!.
['Aaron Lauve', 'Sarah K Mason']
I am writing a research paper on a idea QSym over Sym has a stable basis
[{"from": "human", "value": "I am writing a research paper on a idea QSym over Sym has a stable basis"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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!."}]