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Limit Theorems for Subtree Size Profiles of Increasing Trees

Published online by Cambridge University Press:  25 January 2012

MICHAEL FUCHS
MICHAEL FUCHS*
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 300, Taiwan (e-mail: mfuchs@math.nctu.edu.tw)
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Abstract

Simple families of increasing trees were introduced by Bergeron, Flajolet and Salvy. They include random binary search trees, random recursive trees and random plane-oriented recursive trees (PORTs) as important special cases. In this paper, we investigate the number of subtrees of size k on the fringe of some classes of increasing trees, namely generalized PORTs and d-ary increasing trees. We use a complex-analytic method to derive precise expansions of mean value and variance as well as a central limit theorem for fixed k. Moreover, we propose an elementary approach to derive limit laws when k is growing with n. Our results have consequences for the occurrence of pattern sizes on the fringe of increasing trees.

Keywords

Primary 05C8060F0568W40

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 3 , May 2012 , pp. 412 - 441
Copyright
Copyright © Cambridge University Press 2012

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