Counting monogenic monoids and inverse monoids

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.

arXiv comment9 pages (2 figures, 1 table, updated with number of improvement, to appear in Comm. Alg.)

References in corpus (1)

• Chains of subsemigroups

Cited by in corpus (1)

• E-disjunctive inverse semigroups