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Enumeration of idempotents in planar diagram monoids


Dolinka, I and East, J and Evangelou, A and FitzGerald, D and Ham, N and Hyde, J and Loughlin, N and Mitchell, JD, Enumeration of idempotents in planar diagram monoids, Journal of Algebra, 522 pp. 351-385. ISSN 0021-8693 (2019) [Refereed Article]

Copyright Statement

2018 Elsevier Inc.

DOI: doi:10.1016/j.jalgebra.2018.11.014


We classify and enumerate the idempotents in several planar diagram monoids: namely, the Motzkin, Jones (a.k.a. Temperley-Lieb) and Kauffman monoids. The classification is in terms of certain vertex- and edge-coloured graphs associated to Motzkin diagrams. The enumeration is necessarily algorithmic in nature, and is based on parameters associated to cycle components of these graphs. We compare our algorithms to existing algorithms for enumerating idempotents in arbitrary (regular *-) semigroups, and give several tables of calculated values.

Item Details

Item Type:Refereed Article
Keywords:diagram monoids, partition monoids, Motzkin monoids, Jones monoids, Temperley-Lieb monoids, Kauffman monoids, idempotents, enumeration
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Group theory and generalisations
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:131816
Year Published:2019
Web of Science® Times Cited:5
Deposited By:Mathematics and Physics
Deposited On:2019-04-08
Last Modified:2020-05-20

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