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Enumeration of idempotents in planar diagram monoids

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Dolinka_2018_JA_Enumeration_AAM.pdf (711.4Kb)
Date
15/03/2019
Author
Dolinka, Igor
East, James
Evangelou, Athanasios
FitzGerald, Des
Ham, Nicholas
Hyde, James
Loughlin, Nicholas
Mitchell, James D.
Keywords
Diagram monoids
Partition monoids
Motzkin monoids
Jones monoids
Temperley–Lieb monoids
Kauffman monoids
Idempotents
Enumeration
QA Mathematics
Algebra and Number Theory
T-NDAS
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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
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  • University of St Andrews Research
URL
https://arxiv.org/abs/1507.04838
URI
http://hdl.handle.net/10023/19003

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