Show simple item record

Files in this item

Thumbnail
Name:
Dolinka_2018_JA_Enumeration_AAM.pdf
Size:
711.4Kb
Format:
PDF
View/Open

Enumeration of idempotents in planar diagram monoids

Item metadata

dc.contributor.authorDolinka, Igor
dc.contributor.authorEast, James
dc.contributor.authorEvangelou, Athanasios
dc.contributor.authorFitzGerald, Des
dc.contributor.authorHam, Nicholas
dc.contributor.authorHyde, James
dc.contributor.authorLoughlin, Nicholas
dc.contributor.authorMitchell, James D.
dc.date.accessioned2019-11-26T00:36:47Z
dc.date.available2019-11-26T00:36:47Z
dc.date.issued2019-03-15
dc.identifier256752978
dc.identifier10a3390c-2c4a-4eed-a0de-279100181468
dc.identifier85057241827
dc.identifier000457509500016
dc.identifier.citationDolinka , 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.2018.11.014en
dc.identifier.issn0021-8693
dc.identifier.otherRIS: urn:E02BF2C55AFE99A7A4402D66F255D94A
dc.identifier.otherORCID: /0000-0002-5489-1617/work/73700814
dc.identifier.urihttps://hdl.handle.net/10023/19003
dc.description.abstractWe 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.
dc.format.extent35
dc.format.extent728504
dc.language.isoeng
dc.relation.ispartofJournal of Algebraen
dc.subjectDiagram monoidsen
dc.subjectPartition monoidsen
dc.subjectMotzkin monoidsen
dc.subjectJones monoidsen
dc.subjectTemperley–Lieb monoidsen
dc.subjectKauffman monoidsen
dc.subjectIdempotentsen
dc.subjectEnumerationen
dc.subjectQA Mathematicsen
dc.subjectAlgebra and Number Theoryen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleEnumeration of idempotents in planar diagram monoidsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. St Andrews GAP Centreen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doi10.1016/j.jalgebra.2018.11.014
dc.description.statusPeer revieweden
dc.date.embargoedUntil2019-11-26
dc.identifier.urlhttps://arxiv.org/abs/1507.04838en


This item appears in the following Collection(s)

Show simple item record

Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.