On the Correspondence Between Integer Sequences and Vacillating Tableaux

Zhanar Berikkyzy, Pamela E. Harris, Anna Pun +2

A fundamental identity in the representation theory of the partition algebra is $n^k={\sum }_{\lambda }{f}^{\lambda }{m}_k^{\lambda }$ for $n\ge 2k$, where $\lambda$ ranges over integer partitions of $n$, $f^{\lambda }$ is t…