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Row-strict quasisymmetric Schur functions

Abstract : 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.
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Sarah K Mason, Jeffrey Remmel. Row-strict quasisymmetric Schur functions. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.657-668. ⟨hal-01215042⟩

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