Counting monogenic monoids and inverse monoids
MetadataShow full item record
In 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.
Elliott , L , Levine , A & Mitchell , J D 2023 , ' Counting monogenic monoids and inverse monoids ' , Communications in Algebra , vol. Latest Articles . https://doi.org/10.1080/00927872.2023.2214821
Communications in Algebra
Copyright © 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.
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.
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.