On the degree distribution of the nodes in increasing trees

• Autores: Markus Kuba, Alois Panholzer
• Localización: Journal of Combinatorial Theory, Series A, ISSN 1096-0899, Vol. 114, Nº. 4, 2007, págs. 597-618
• Idioma: inglés
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• Resumen

  • Simple families of increasing trees can be constructed from simply generated tree families, if one considers for every tree of size n all its increasing labellings, i.e., labellings of the nodes by distinct integers of the set {1,¿,n} in such a way that each sequence of labels along any branch starting at the root is increasing. Three such tree families are of particular interest: recursive trees, plane-oriented recursive trees and binary increasing trees. We study the quantity degree of node j in a random tree of size n and give closed formulae for the probability distribution and all factorial moments for those subclass of tree families, which can be constructed via a tree evolution process. Furthermore limiting distribution results of this parameter are given, which completely characterize the phase change behavior depending on the growth of j compared to n