On the Average Height of b-Balanced Ordered Trees
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Abstract:
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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Journal title
volume 3 issue None
pages 175- 218
publication date 2004-11
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