Anne Schilling: An insertion algorithm on multiset partitions

Abstract

We provide an insertion algorithm from generalized permutations (or two-line arrays subject to certain conditions) and pairs of standard Young tableaux and multiset tableaux of the same shape. If we insert the propagating blocks of partition diagrams we get natural sets of tableaux and the number of these tableaux of a fixed shape are equal to the dimensions of irreducible representations indexed by the same shape. This is joint work with Laura Colmenarejo, Rosa Orellana, Franco Saliola and Mike Zabrocki.