In Sections 4 and 5 we introduce an insertion algorithm and use it to provide an analogue of the Robinson-Schensted-Knuth algorithm as well as a generalized Cauchy identity.
The Robinson-Schensted-Knuth (RSK) Algorithm is a bijection between matrices with non-negative integer entries and pairs of semi-standard Young tableaux.
Properties of the nonsymmetric Robinson-Schensted-Knuth algorithm.
A decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth algorithm.
The fundamental operation of the Robinson-Schensted-Knuth
(1970) (RSK) algorithm is Schensted insertion which is a procedure for inserting a positive integer k into a SSYT T.
Proof: Consider the Robinson-Schensted-Knuth
(RSK) correspondence between SSYTs with no more than r rows filled with [x.
Sagan (12) and Worley (20) have introduced the Sagan-Worley correspondence, another analog of Robinson-Schensted-Knuth correspondence for shifted tableaux.
Haiman's construction can be viewed as a shifted analog of the Robinson-Schensted-Knuth correspondence.