The number of monounary algebras (Q647328)

The authors deal with finite monounary algebras. To such algebras there correspond directed graphs where each vertex has outdegree \(1\). In the paper, the method of generating functions is applied. Using results of \textit{R. Otter} [Ann. Math. (2) 49, 583--599 (1948; Zbl 0032.12601)] concerning the number of trees, the following asymptotically presented formula is proved: Let \(M_n\), for a positive integer \(n\), denote the number of non-isomorphic monounary algebras of size \(n\). Then \(\log_{\alpha}M_n\sim n\), where \(\alpha\sim 2.955765\).