Descendants in increasing trees
type: Item
instance of: scholarly article
title: Descendants in increasing trees
zbMATH Open document ID: 1080.05019
author: Markus Kuba
author: Alois Panholzer
published in: The Electronic Journal of Combinatorics
publication date: 2006-01-31T00:00:00Z
full work available at URL: https://eudml.org/doc/125517
full work available at URL: v13i1r8.html
review text: Summary: 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 \(\{1,\dots, n\}\) 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 number of descendants of node \(j\) in a random tree of size \(n\) and give closed formulae for the probability distribution and all factorial moments for those subclasses of tree families, which can be constructed via an insertion process. Furthermore limiting distribution results of this parameter are given.
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 5002941
zbMATH Keywords: recursive trees
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5002941