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arxiv: 1507.04838 · v3 · pith:IXWVQGZKnew · submitted 2015-07-17 · 🧮 math.CO

Enumeration of idempotents in planar diagram monoids

Igor Dolinka , James East , Athanasios Evangelou , Desmond Fitzgerald , Nicholas Ham , James Hyde , Nicholas Loughlin , James Mitchell This is my paper
classification 🧮 math.CO
keywords idempotentsmonoidsalgorithmsassociateddiagramenumerationgraphsmotzkin
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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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    math.RT 2022-06 unverdicted novelty 5.0

    Sandwich cellularity is presented as a version of cell theory for algebras and applied to Hecke algebras plus monoid and diagram algebras.