Enumeration of idempotents in planar diagram monoids

JOURNAL OF ALGEBRA

卷:522

Article

Dolinka, Igor¹  East, James²  Evangelou, Athanasios³  FitzGerald, Des³  Ham, Nicholas³  Hyde, James⁴  Loughlin, Nicholas⁵  Mitchell, James D.⁴ 

[1] Univ Novi Sad, Dept Math & Informat, Trg Dositeja Obradovica 4, Novi Sad 21101, Serbia

[2] Univ Western Sydney, Sch Comp Engn & Math, Ctr Res Math, Locked Bag 1797, Penrith, NSW 2751, Australia

[3] Univ Tasmania, Sch Math & Phys, Private Bag 37, Hobart, Tas 7001, Australia

[4] Univ St Andrews, Sch Math & Stat, St Andrews KY16 9SS, Fife, Scotland

[5] Newcastle Univ, Sch Math & Stat, Newcastle NE1 7RU, England

关键词: Diagram monoids;    Partition monoids;    Motzkin monoids;   

DOI  :  10.1016/j.jalgebra.2018.11.014

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free