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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.issued2023-11-01
dc.identifier286136026
dc.identifier3e5f2dd3-cb3a-402e-b06a-38b935661132
dc.identifier85161313740
dc.identifier.citationElliott , L , Levine , A & Mitchell , J D 2023 , ' Counting monogenic monoids and inverse monoids ' , Communications in Algebra , vol. 51 , no. 11 , pp. 4654-4661 . https://doi.org/10.1080/00927872.2023.2214821en
dc.identifier.issn0092-7872
dc.identifier.urihttps://hdl.handle.net/10023/27702
dc.descriptionFunding: The 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.format.extent1074166
dc.language.isoeng
dc.relation.ispartofCommunications in Algebraen
dc.subjectInverse semigroupen
dc.subjectMonogenic semigroupen
dc.subjectTransformation semigroupen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectMCCen
dc.subject.lccQAen
dc.titleCounting monogenic monoids and inverse monoidsen
dc.typeJournal articleen
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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