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Enumeration of idempotents in planar diagram monoids

Dolinka, I, East, J, Evangelou, A, FitzGerald, D, Ham, N, Hyde, J, Loughlin, N and Mitchell, JD 2019 , 'Enumeration of idempotents in planar diagram monoids' , Journal of Algebra, vol. 522 , pp. 351-385 , doi: 10.1016/j.jalgebra.2018.11.014.

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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 Type: Article
Authors/Creators:Dolinka, I and East, J and Evangelou, A and FitzGerald, D and Ham, N and Hyde, J and Loughlin, N and Mitchell, JD
Keywords: diagram monoids, partition monoids, Motzkin monoids, Jones monoids, Temperley-Lieb monoids, Kauffman monoids, idempotents, enumeration
Journal or Publication Title: Journal of Algebra
Publisher: Academic Press Inc Elsevier Science
ISSN: 0021-8693
DOI / ID Number: 10.1016/j.jalgebra.2018.11.014
Copyright Information:

© 2018 Elsevier Inc.

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