Tableaux and matrix correspondences

AbstractThe Robinson-Schensted correspondence, a bijection between nonnegative matrices and pair of tableaux, is investigated. The representation, in the tableau, of the dihedral symmetries of the matrix are derived in a simple manner using a shape-preserving anti-isomorphism of the platic monoid. The Robinson-Schensted correspondence is shown to be equivalent to the Hillman-Grassl bijection between reverse plane partitions and tabloids. A generalized insertion method for the Robinson-Schensted correspondence is obtained