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QSym over Sym has a stable basis |
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| Authors: | Aaron Lauve Sarah K Mason |
| Institution: | a Department of Mathematics & Statistics, Loyola University Chicago, Chicago, IL 60660, United States b Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109, United States |
| 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: | Quasisymmetric functions Symmetric functions Free modules Inverting compositions |
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