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QSym over Sym has a stable basis
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010) Cet article a éte moissonné depuis la source Episciences

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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 $n!$. 
@article{DMTCS_2010_special_259_a61,
     author = {Lauve, Aaron and Mason, Sarah K},
     title = {QSym over {Sym} has a stable basis},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2010},
     volume = {DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)},
     doi = {10.46298/dmtcs.2866},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2866/}
}
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Lauve, Aaron; Mason, Sarah K. QSym over Sym has a stable basis. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi: 10.46298/dmtcs.2866

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