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arXiv · 2303.12387

Counting monogenic monoids and inverse monoids

L. Elliott·A. Levine·J. D. Mitchell
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Abstract

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.

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BibTeXRIS

L. Elliott, A. Levine, J. D. Mitchell. 2023-03-22. Counting monogenic monoids and inverse monoids. https://doi.org/10.1080/00927872.2023.2214821

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