Skew row-strict quasisymmetric Schur functions
| Autor: | Mason, Sarah K., Niese, Elizabeth |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | J.Algebr.Comb 42 (2015) 763--791 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 30 pages, 18 figures, updated from journal article version to incorporate variables in Theorem 12 |
| Databáze: | arXiv |
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