A new bijection on rooted forests (Q686461)

A semilabelled tree is a rooted tree with labelled leaves. Earlier, the author and \textit{L. A. Székely} [Adv. Appl. Math. 10, No. 4, 488-496 (1989; Zbl 0723.05046)] gave a bijection, involving antilexicographic order, between semilabelled trees and certain partitions. The author of the present paper extends this earlier work by giving a bijection between semilabelled forests and certain multisets. Various formulas for the number of semilabelled and labelled forests with certain properties follow readily as consequences of the bijection.