Counting monogenic monoids and inverse monoids
Date
01/11/2023Metadata
Show full item recordAbstract
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.
Citation
Elliott , 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/10.1080/00927872.2023.2214821
Publication
Communications in Algebra
Status
Peer reviewed
ISSN
0092-7872Type
Journal article
Description
Funding: 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.Collections
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