#### Title

The Rook Partition Algebra

#### Document Type

Article

#### Publication Date

2-1-2006

#### Published In

Journal Of Combinatorial Theory Series A

#### Abstract

The rook partition algebra RPk(x) is a generically semisimple algebra that arises from looking at what commutes with the action of the symmetric group Sn on U⊗k, where U is the direct sum of the natural representation and the trivial representation of Sn. We give a combinatorial description of this algebra, construct its irreducible representations, and exhibit a Murnaghan–Nakayama formula to compute certain character values.

#### Recommended Citation

Cheryl Grood.
(2006).
"The Rook Partition Algebra".
*Journal Of Combinatorial Theory Series A.*
Volume 113,
Issue 2.
325-351.
DOI: 10.1016/j.jcta.2005.03.006

https://works.swarthmore.edu/fac-math-stat/15