\input zb-basic
\input zb-ioport
\iteman{io-port 05977554}
\itemau{Horv\'ath, G\'abor; K\'atai-Urb\'an, Kamilla; Pach, P\'eter P\'al; Pluh\'ar, Gabriella; Szab\'o, Csaba; Pongr\'acz, Andr\'as}
\itemti{The number of monounary algebras.}
\itemso{Algebra Univers. 66, No. 1-2, 81-83 (2011).}
\itemab
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 {\it 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 $\alpha\sim 2.955765$.
\itemrv{Danica Jakubikov\'a-Studenovsk\'a (Ko\v sice)}
\itemcc{}
\itemut{monounary algebra; generating function}
\itemli{doi:10.1007/s00012-011-0147-y}
\end