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arXiv · 2105.13421

Skew row-strict quasisymmetric Schur functions

Sarah K. Mason·Elizabeth Niese
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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.

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Sarah K. Mason, Elizabeth Niese. 2021-05-27. Skew row-strict quasisymmetric Schur functions. https://arxiv.org/abs/2105.13421

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