2015/07/17 by Igor Dolinka, Dolinka, Igor, James East +13
Computer Science · Mathematics · #05A18 (Secondary) #05E15 (Primary) #20M17 #20M20 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #semigroups and automata theory
paper · doi:10.48550/arxiv.1507.04838
openalex publication_date 2015/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.