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Enumerating transformation semigroups

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dc.contributor.authorEast, James
dc.contributor.authorEgri-Nagy, Attila
dc.contributor.authorMitchell, James D.
dc.date.accessioned2018-04-03T23:34:25Z
dc.date.available2018-04-03T23:34:25Z
dc.date.issued2017-08
dc.identifier.citationEast , J , Egri-Nagy , A & Mitchell , J D 2017 , ' Enumerating transformation semigroups ' , Semigroup Forum , vol. 95 , no. 1 , pp. 109-125 . https://doi.org/10.1007/s00233-017-9869-2en
dc.identifier.issn0037-1912
dc.identifier.otherPURE: 250016662
dc.identifier.otherPURE UUID: e9b23682-41b5-49e8-a05f-d000b5e77793
dc.identifier.otherScopus: 85016963735
dc.identifier.otherWOS: 000407398800006
dc.identifier.otherORCID: /0000-0002-5489-1617/work/73700782
dc.identifier.urihttp://hdl.handle.net/10023/13064
dc.descriptionThis work was partially supported by the NeCTAR Research Cloud, an initiative of the Australian Government’s Super Science scheme and the Education Investment Fund; and by the EU Project BIOMICS (Contract Number CNECT-ICT-318202).en
dc.description.abstractWe describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation semigroups up to degree 4. Classification of these semigroups up to conjugacy, isomorphism and anti-isomorphism, by size and rank, provides a solid base for further investigations of transformation semigroups.
dc.format.extent17
dc.language.isoeng
dc.relation.ispartofSemigroup Forumen
dc.rightsCopyright © 2017, Springer Science+Business Media New York This work is 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/10.1007/s00233-017-9869-2en
dc.subjectComputational enumerationen
dc.subjectIdeal structureen
dc.subjectMultiplication tableen
dc.subjectTransformation semigroupen
dc.subjectQA Mathematicsen
dc.subjectAlgebra and Number Theoryen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleEnumerating transformation semigroupsen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.1007/s00233-017-9869-2
dc.description.statusPeer revieweden
dc.date.embargoedUntil2018-04-03
dc.identifier.urlhttps://arxiv.org/abs/1403.0274en


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