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Central Limit Theorems for Additive Tree Parameters with Small Toll Functions

Published online by Cambridge University Press:  08 September 2014

STEPHAN WAGNER
STEPHAN WAGNER*
Affiliation:
Department of Mathematical Sciences, Stellenbosch University, 7602 Stellenbosch, South Africa (e-mail: [email protected])
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Abstract

We call a tree parameter additive if it can be determined recursively as the sum of the parameter values of all branches, plus a certain toll function. In this paper, we prove central limit theorems for very general toll functions, provided that they are bounded and small on average. Simply generated families of trees are considered as well as Pólya trees, recursive trees and binary search trees, and the results are illustrated by several examples of parameters for which we prove normal or log-normal limit laws.

Keywords

Primary 60C05Secondary 05A1605C0505C8060F05
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 24 , Special Issue 1: Honouring the Memory of Philippe Flajolet - Part 3 , January 2015 , pp. 329 - 353
Copyright
Copyright © Cambridge University Press 2014 

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