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Counting monogenic monoids and inverse monoids

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dc.contributor.authorElliott, L.
dc.contributor.authorLevine, A.
dc.contributor.authorMitchell, James David
dc.date.accessioned2023-05-31T09:30:14Z
dc.date.available2023-05-31T09:30:14Z
dc.date.issued2023-05-23
dc.identifier.citationElliott , L , Levine , A & Mitchell , J D 2023 , ' Counting monogenic monoids and inverse monoids ' , Communications in Algebra , vol. Latest Articles . https://doi.org/10.1080/00927872.2023.2214821en
dc.identifier.issn0092-7872
dc.identifier.otherPURE: 286136026
dc.identifier.otherPURE UUID: 3e5f2dd3-cb3a-402e-b06a-38b935661132
dc.identifier.otherScopus: 85161313740
dc.identifier.urihttp://hdl.handle.net/10023/27702
dc.descriptionThe second and third authors would like to thank the London Mathematical Society, the Heilbronn Institute for Mathematical Research, and the University of St Andrews, for their support of this work.en
dc.description.abstractIn this short note, we show that the number of monogenic submonoids of the full transformation monoid of degree n for n>0, equals the sum of the number of cyclic subgroups of the symmetric groups on 1 to n points. We also prove an analogous statement for monogenic subsemigroups of the finite full transformation monoids, as well as monogenic inverse submonoids and subsemigroups of the finite symmetric inverse monoids.
dc.format.extent8
dc.language.isoeng
dc.relation.ispartofCommunications in Algebraen
dc.rightsCopyright © 2023 The Author(s). Published with license by Taylor and Francis Group, LLC.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.en
dc.subjectInverse semigroupen
dc.subjectMonogenic semigroupen
dc.subjectTransformation semigroupen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectMCPen
dc.subject.lccQAen
dc.titleCounting monogenic monoids and inverse monoidsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1080/00927872.2023.2214821
dc.description.statusPeer revieweden


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