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Enumeration of idempotents in diagram semigroups and algebras
Citation
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
Abstract
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 |
| Downloads: | 0 |
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