Properties of the nonsymmetric RobinsonSchenstedKnuth algorithm
We introduce a generalization of the RobinsonSchenstedKnuth insertion algorithm for semi-standard augmented fillings whose basement is an arbitrary permutation ??S n . If ? is the identity, then our insertion algorithm reduces to the insertion algorithm introduced by the second author (Smin. Lothar. Comb. 57:B57e, 2006) for semi-standard augmented fillings and if ? is the reverse of the identity, then our insertion algorithm reduces to the original RobinsonSchenstedKnuth 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 ? 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, ageneralization of Knuths 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 ?.
permutations demazure atoms symmetric functions nonsymmetric macdonald polynomials permuted basement fillings