Mathematics Colloquia and Seminars

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Vacillating tableaux are sequences of integer partitions that satisfy specific conditions.  The concept of vacillating tableaux stems from the representation theory of the partition algebra and the combinatorial theory of crossings and nestings of matchings and set partitions. Using a combination of RSK insertion and jeu de taquin, Halverson and Lewandowski constructed a bijection $DI_n^k$ that associates integer sequences to pairs of standard Young tableaux and vacillating tableaux.

We characterize integer sequences corresponding to vacillating tableaux under the map $DI_n^k$ of certain shapes. Additionally, we explore multiple combinatorial identities and integer sequences relating to the number of vacillating tableaux, simplified vacillating tableaux, and limiting vacillating tableaux. This talk is based on joint work with Z. Berikkyzy, P. E. Harris, A. Pun and C. Yan.