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Enumeration of idempotents in planar diagram monoids
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dc.contributor.author | Dolinka, Igor | |
dc.contributor.author | East, James | |
dc.contributor.author | Evangelou, Athanasios | |
dc.contributor.author | FitzGerald, Des | |
dc.contributor.author | Ham, Nicholas | |
dc.contributor.author | Hyde, James | |
dc.contributor.author | Loughlin, Nicholas | |
dc.contributor.author | Mitchell, James D. | |
dc.date.accessioned | 2019-11-26T00:36:47Z | |
dc.date.available | 2019-11-26T00:36:47Z | |
dc.date.issued | 2019-03-15 | |
dc.identifier | 256752978 | |
dc.identifier | 10a3390c-2c4a-4eed-a0de-279100181468 | |
dc.identifier | 85057241827 | |
dc.identifier | 000457509500016 | |
dc.identifier.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 | en |
dc.identifier.issn | 0021-8693 | |
dc.identifier.other | RIS: urn:E02BF2C55AFE99A7A4402D66F255D94A | |
dc.identifier.other | ORCID: /0000-0002-5489-1617/work/73700814 | |
dc.identifier.uri | https://hdl.handle.net/10023/19003 | |
dc.description.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. | |
dc.format.extent | 35 | |
dc.format.extent | 728504 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Algebra | en |
dc.subject | Diagram monoids | en |
dc.subject | Partition monoids | en |
dc.subject | Motzkin monoids | en |
dc.subject | Jones monoids | en |
dc.subject | Temperley–Lieb monoids | en |
dc.subject | Kauffman monoids | en |
dc.subject | Idempotents | en |
dc.subject | Enumeration | en |
dc.subject | QA Mathematics | en |
dc.subject | Algebra and Number Theory | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Enumeration of idempotents in planar diagram monoids | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. St Andrews GAP Centre | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1016/j.jalgebra.2018.11.014 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2019-11-26 | |
dc.identifier.url | https://arxiv.org/abs/1507.04838 | en |
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