Sarah K Mason ; Jeffrey Remmel - Row-strict quasisymmetric Schur functions

dmtcs:2942 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2942
Row-strict quasisymmetric Schur functions

Authors: Sarah K Mason 1; Jeffrey Remmel 2

  • 1 Department of Mathematics
  • 2 Department of Mathematics [Univ California San Diego]

Haglund, Luoto, Mason, and van Willigenburg introduced a basis for quasisymmetric functions called the $\textit{quasisymmetric Schur function basis}$ which are generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through reverse column-strict tableaux. We introduce a new basis for quasisymmetric functions called the $\textit{row-strict quasisymmetric Schur function basis}$ which are generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through row-strict tableaux. We describe the relationship between this new basis and other known bases for quasisymmetric functions, as well as its relationship to Schur polynomials. We obtain a refinement of the omega transform operator as a result of these relationships.


Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: symmetric and quasisymmetric functions,omega operator,Schur functions,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Combinatorial Structures for Permutation Enumeration and Macdonald Polynomials; Funder: National Science Foundation; Code: 0654060
  • PostDoctoral Research Fellowship; Funder: National Science Foundation; Code: 0603351

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Source : ScholeXplorer IsRelatedTo DOI 10.1006/aima.1996.0026
  • 10.1006/aima.1996.0026
On Posets and Hopf Algebras

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