Shuffle Invariance of the Super-RSK Algorithm

Abstract

As in the (k,l)-RSK (Robinson–Schensted–Knuth) of A. Berele and A. Regev (1987, Adv. Math.64, 118–175), other super-RSK algorithms can be applied to sequences of variables from the set {t1,…,tk,u1,…,ul}, where t1<⋯<tk and u1<⋯<ul. While the (k,l)-RSK is the case where ti<uj for all i and j, these other super-RSK's correspond to all the [formula] shuffles of the t's and u's satisfying the above restrictions that t1<⋯<tk and u1<⋯<ul. We show that the shape of the tableaux produced by any such super-RSK is independent of the particular shuffle of the t's and u's.