RSK Insertion for Set Partitions and Diagram Algebras
| dc.creator | Halverson, Tom | |
| dc.creator | Lewandowski, Tim | |
| dc.date | 2005-07-01 | |
| dc.date.accessioned | 2026-07-07T05:21:19Z | |
| dc.date.available | 2026-07-07T05:21:19Z | |
| dc.description | 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 $n^k = \sum_λf^λm_k^λ$, where the sum is over partitions $λ$ of $n$, $f^λ$ is the number of standard tableaux of shape $λ$, and $m_k^λ$ is the number of "vacillating tableaux" of shape $λ$ and length $2k$. Our proof uses a combination of Robinson-Schensted-Knuth insertion and jeu de taquin. The second identity is $B(2k) = \sum_λ(m_k^λ)^2$, where $B(2k)$ is the number of set partitions of $\{1, >..., 2k\}$. We show that this insertion restricts to work for the diagram algebras which appear as subalgebras of the partition algebra: the Brauer, Temperley-Lieb, planar partition, rook monoid, planar rook monoid, and symmetric group algebras. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507026 | |
| dc.identifier | http://arxiv.org/abs/math/0507026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75649 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.subject | 05E10 | |
| dc.title | RSK Insertion for Set Partitions and Diagram Algebras | |
| dc.type | text |