Sarah K Mason ; Jeffrey Remmel

Rowstrict 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
Rowstrict quasisymmetric Schur functions
Authors: Sarah K Mason ^{1}; Jeffrey Remmel ^{2}
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Sarah K Mason;Jeffrey Remmel
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 columnstrict tableaux. We introduce a new basis for quasisymmetric functions called the $\textit{rowstrict quasisymmetric Schur function basis}$ which are generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through rowstrict 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.