A solution to a problem of Dénes: A bijection between trees and factorizations of cyclic permutations
\textit{J. Dénes} [Publ. Math. Inst. Hung. Acad. Sci. 4, 63-70 (1959; Zbl 0092.011)] proved that the set \(T_ n\) of labelled trees on n vertices and the set of representations of a given cyclic permutation (from the symmetric group of order n) as a product of n-1 transpositions have the same cardinality, and posed the question of finding a direct bijection between these two sets. This note provides such a bijection.
scientific article; zbMATH DE number 4099321