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Journal of Algebraic Combinatorics

, Volume 42, Issue 3, pp 763–791 | Cite as

Skew row-strict quasisymmetric Schur functions

  • Sarah K. Mason
  • Elizabeth Niese
Article

Abstract

Mason and Remmel introduced a basis for quasisymmetric functions known as the row-strict quasisymmetric Schur functions. This basis is generated combinatorially by fillings of composition diagrams that are analogous to the row-strict tableaux that generate Schur functions. We introduce a modification known as Young row-strict quasisymmetric Schur functions, which are generated by row-strict Young composition fillings. After discussing basic combinatorial properties of these functions, we define a skew Young row-strict quasisymmetric Schur function using the Hopf algebra of quasisymmetric functions and then prove this is equivalent to a combinatorial description. We also provide a decomposition of the skew Young row-strict quasisymmetric Schur functions into a sum of Gessel’s fundamental quasisymmetric functions and prove a multiplication rule for the product of a Young row-strict quasisymmetric Schur function and a Schur function.

Keywords

Quasisymmetric functions Schur functions Composition tableaux Littlewood–Richardson rule 

Notes

Acknowledgments

Both authors were partially supported by a Wake Forest University Collaboration Pilot Grant.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsWake Forest UniversityWinston-SalemUSA
  2. 2.Department of MathematicsMarshall UniversityHuntingtonUSA

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