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Enumeration of idempotents in diagram semigroups and algebras


Dolinka, I and East, J and Evangelou, A and FitzGerald, D and Ham, N and Hyde, J and Loughlin, N, Enumeration of idempotents in diagram semigroups and algebras, Journal of Combinatorial Theory, Series A, 131 pp. 119-152. ISSN 0097-3165 (2015) [Refereed Article]

Copyright Statement

Copyright 2015 Elsevier

DOI: doi:10.1016/j.jcta.2014.11.008


We give a characterisation of the idempotents of the partition monoid, and use this to enumerate the idempotents in the finite partition, Brauer and partial Brauer monoids, giving several formulae and recursions for the number of idempotents in each monoid as well as various R-, L- and D-classes. We also apply our results to determine the number of idempotent basis elements in the finite dimensional partition, Brauer and partial Brauer algebras.

Item Details

Item Type:Refereed Article
Keywords:partition monoids, partition algebras, Brauer monoids, Brauer algebras, idempotents, enumeration
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Combinatorics and discrete mathematics (excl. physical combinatorics)
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Evangelou, A (Mr Athanasios Evangelou-Oost)
UTAS Author:FitzGerald, D (Dr Des FitzGerald)
UTAS Author:Ham, N (Mr Nicholas Ham)
ID Code:98887
Year Published:2015
Web of Science® Times Cited:16
Deposited By:Mathematics and Physics
Deposited On:2015-03-05
Last Modified:2017-11-15

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