Aaron Lauve ; Sarah K Mason - QSym over Sym has a stable basis

dmtcs:2866 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2866
QSym over Sym has a stable basisArticle

Authors: Aaron Lauve 1; Sarah K Mason 2

  • 1 Department of Mathematics [Austin]
  • 2 Department of Mathematics

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 $n!$.

https://doi.org/10.46298/dmtcs.2866
Source: HAL:hal-01186295v1
Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: quasisymmetric functions,symmetric functions,free modules,compositions,inverting compositions,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • PostDoctoral Research Fellowship; Funder: National Science Foundation; Code: 0603351

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