Geodesic
Skew row-strict quasisymmetric Schur functions
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 763-791.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

S. Mason and J. Remmel [Ann. Comb. 18, No. 1, 127--148 (2014; Zbl 1297.05241)] 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.
Classification : 05E05, 05E10
Keywords: quasisymmetric functions, Schur functions, composition tableaux, Littlewood-Richardson rule 
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     title = {Skew row-strict quasisymmetric {Schur} functions},
     journal = {Journal of Algebraic Combinatorics},
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     publisher = {mathdoc},
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     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2015__42_3_a6/}
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Mason, Sarah K.; Niese, Elizabeth. Skew row-strict quasisymmetric Schur functions. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 763-791. http://geodesic.mathdoc.fr/item/JAC_2015__42_3_a6/