Ebook: Enumeration of idempotents in planar diagram monoids
Author: Igor Dolinka James East Des FitzGerald Nicholas Ham James Hyded Nicholas Loughlin James D. Mitchell
- Genre: Mathematics // Algebra
- Tags: Diagram monoids partition monoids Motzkin monoids Jones monoids Temperley-Lieb monoids Kauffman monoids idempotents enumeration. MSC: 05E15 20M20 20M17 05A18.
- Year: 2019
- Publisher: Journal of Algebra
- Language: English
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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.
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