Enumeration of idempotents in planar diagram monoids
journal contribution
posted on 2023-05-20, 02:35authored byDolinka, I, East, J, Evangelou, A, Desmond FitzGerald, Ham, N, Hyde, J, Loughlin, N, Mitchell, JD
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.
History
Publication title
Journal of Algebra
Volume
522
Pagination
351-385
ISSN
0021-8693
Department/School
School of Natural Sciences
Publisher
Academic Press Inc Elsevier Science
Place of publication
525 B St, Ste 1900, San Diego, USA, Ca, 92101-4495