A solution to a problem of Dénes: A bijection between trees and factorizations of cyclic permutations
type: Item
instance of: scholarly article
title: A solution to a problem of Dénes: A bijection between trees and factorizations of cyclic permutations
zbMATH Open document ID: 0672.05022
DOI: 10.1016/S0195-6698(89)80028-9
author: Paul Moszkowski
published in: European Journal of Combinatorics
publication date: 1989-01-01T00:00:00Z
review text: \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.
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05A05
zbMATH DE Number: 4099321
zbMATH Keywords: labelled trees
zbMATH Keywords: cyclic permutation
zbMATH Keywords: bijection
reviewed by: Neil H. Williams
MaRDI profile type: Publication
Wikidata QID: Q114121534
cites work: Q3267408
cites work: Q5721212
cites work: Q5633999
full work available at URL: s0195-6698(89)80028-9
OpenAlex ID: W1974527570
description: scientific article; zbMATH DE number 4099321