The partition algebra CAk (n) is the centralizer algebra of Sn acting on the k-fold tensor
product V⊗ k of its n-dimensional permutation representation V. The partition algebra CAk+ …

The symmetric group S _n and the partition algebra P _k (n) centralize one another in their
actions on the k-fold tensor power M _n^ ⊗ k of the n-dimensional permutation module M _n …

In this paper we develop a new groupoid-based structure theory for the class of regular⁎-
semigroups. This class occupies something of a 'sweet spot'between the important classes …

We construct generalizations P mn (Q) of the partition algebra P n (Q)(Martin PP 1996 J.
Algebra 183 319), facilitating a representation theoretic approach to the n-site transfer matrix …

The partition algebra P _k (n) P k (n) and the symmetric group S _n S n are in Schur–Weyl
duality on the k-fold tensor power M _n^ ⊗ k M n⊗ k of the permutation module M _n M n of S …

Assume M n is the n‐dimensional permutation module for the symmetric group S n, and let
M n⊗ k be its k‐fold tensor power. The partition algebra P k (n) maps surjectively onto the …

Abstract We generalize the Robinson–Schensted–Knuth algorithm to the insertion of two
row arrays of multisets. This generalization leads to new enumerative results that have …

arxiv:2304.07657v2 [math.CO] 29 Dec 2023 Page 1 arxiv:2304.07657v2 [math.CO] 29 Dec
2023 Identities for vacillating tableaux via growth diagrams C. Krattenthaler Fakultät für …

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 …

We describe various diagram algebras and their representation theory using cellular
algebras of Graham and Lehrer and the decomposition into half diagrams. In particular, we …