Title: Limit Theorems for Subtree Size Profiles of Increasing Trees
Authors: Fuchs, Michael
應用數學系
Department of Applied Mathematics
Issue Date: 1-May-2012
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.
URI: http://hdl.handle.net/11536/16006
ISSN: 0963-5483
Journal: COMBINATORICS PROBABILITY & COMPUTING
Volume: 21
Issue: 3
End Page: 412
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