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Kemp R. On the Average Height of b-Balanced Ordered Trees. JIRSS. 2004; 3 (2) :175-218
URL: http://jirss.irstat.ir/article-1-110-en.html

Abstract:   (4458 Views)
An ordered tree with height h is b-balanced if all its leaves have a level l with h − b <= l <= h, where at least one leaf has a level equal to h − b. For large n, we shall compute asymptotic equivalents to the number of all b-balanced ordered trees with n nodes and of all such trees with height h. Furthermore, assuming that all b-balanced ordered trees with n nodes are equally likely, we shall determine the exact asymptotic behaviour of the average height of such a tree together with the variance.
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Subject: 60: Probability theory and stochastic processes
Received: 2011/08/26 | Accepted: 2015/09/12

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