Enumeration of idempotents in planar diagram monoids

Dolinka, Igor; East, James; Evangelou, Athanasios; FitzGerald, Des; Ham, Nicholas; Hyde, James; Loughlin, Nicholas; Mitchell, James D.

View/Open

Dolinka_2018_JA_Enumeration_AAM.pdf (711.4Kb)

Date

15/03/2019

Altmetrics Handle Statistics

Altmetrics DOI Statistics

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.

Citation

Dolinka , I , East , J , Evangelou , A , FitzGerald , D , Ham , N , Hyde , J , Loughlin , N & Mitchell , J D 2019 , ' Enumeration of idempotents in planar diagram monoids ' , Journal of Algebra , vol. 522 , pp. 351-385 . https://doi.org/10.1016/j.jalgebra.2018.11.014

Publication

Journal of Algebra

Status

Peer reviewed

DOI

https://doi.org/10.1016/j.jalgebra.2018.11.014

ISSN

0021-8693

Type

Journal article

Rights

Copyright © 2018 Elsevier Inc. All rights reserved. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jalgebra.2018.11.014

Collections

University of St Andrews Research

URL

https://arxiv.org/abs/1507.04838

URI

http://hdl.handle.net/10023/19003