RSK Insertion for Set Partitions and Diagram Algebras

Tom Halverson, Tim Lewandowski

We give combinatorial proofs of two identities from the representation theory of the partition algebra $C{A}_k(n),n\ge 2k$. The first is $n^k={\sum }_{\lambda }{f}^{\lambda }{m}_k^{\lambda }$, where the sum is o…