Limit Theorems for Subtree Size Profiles of Increasing Trees
2012 ◽
Vol 21
(3)
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pp. 412-441
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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.
2002 ◽
Vol 11
(6)
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pp. 587-597
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1991 ◽
Vol 2
(3)
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pp. 303-315
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2002 ◽
Vol 32
(1)
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pp. 152-171
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2005 ◽
Vol 37
(02)
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pp. 321-341
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Keyword(s):
Keyword(s):
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