Enumeration of idempotents in planar diagram monoids
Combinatorics
2018-08-13 v3
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.
Keywords
Cite
@article{arxiv.1507.04838,
title = {Enumeration of idempotents in planar diagram monoids},
author = {Igor Dolinka and James East and Athanasios Evangelou and Desmond FitzGerald and Nicholas Ham and James Hyde and Nicholas Loughlin and James Mitchell},
journal= {arXiv preprint arXiv:1507.04838},
year = {2018}
}
Comments
Majorly revised (new title, new abstract, one additional author), 24 pages, 6 figures, 8 tables, 5 algorithms