Properties of the nonsymmetric Robinson–Schensted–Knuth algorithm |
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Authors: | James Haglund Sarah Mason Jeffrey Remmel |
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Institution: | 1. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104, USA 2. Department of Mathematics, Wake Forest University, Winston-Salem, NC, 27109, USA 3. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093-0112, USA
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Abstract: | We introduce a generalization of the Robinson–Schensted–Knuth insertion algorithm for semi-standard augmented fillings whose basement is an arbitrary permutation σ∈S n . If σ is the identity, then our insertion algorithm reduces to the insertion algorithm introduced by the second author (Sémin. Lothar. Comb. 57:B57e, 2006) for semi-standard augmented fillings and if σ is the reverse of the identity, then our insertion algorithm reduces to the original Robinson–Schensted–Knuth row insertion algorithm. We use our generalized insertion algorithm to obtain new decompositions of the Schur functions into nonsymmetric elements called generalized Demazure atoms (which become Demazure atoms when σ is the identity). Other applications include Pieri rules for multiplying a generalized Demazure atom by a complete homogeneous symmetric function or an elementary symmetric function, a generalization of Knuth’s correspondence between matrices of non-negative integers and pairs of tableaux, and a version of evacuation for composition tableaux whose basement is an arbitrary permutation σ. |
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