Shuffle Invariance of the Super-RSK Algorithm

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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 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. © 2002 Elsevier Science (USA).

Document Type: Research Article

Affiliations: Department of Theoretical Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel

Publication date: January 1, 2002

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