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Enumeration of idempotents in planar diagram monoids
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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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Abstract
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 |
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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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