James Haglund ; Sarah Mason ; Kurt Luoto ; Steph van Willigenburg
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Quasisymmetric Schur functions
dmtcs:3605 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2008,
DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
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https://doi.org/10.46298/dmtcs.3605
Quasisymmetric Schur functions
Authors: James Haglund 1; Sarah Mason 2; Kurt Luoto 3; Steph van Willigenburg 4
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James Haglund;Sarah Mason;Kurt Luoto;Steph van Willigenburg
1 University of Pennsylvania
2 Davidson College
3 University of Washington [Seattle]
4 University of British Columbia
We introduce a new basis for the algebra of quasisymmetric functions that naturally partitions Schur functions, called quasisymmetric Schur functions. We describe their expansion in terms of fundamental quasisymmetric functions and determine when a quasisymmetric Schur function is equal to a fundamental quasisymmetric function. We conclude by describing a Pieri rule for quasisymmetric Schur functions that naturally generalizes the Pieri rule for Schur functions.