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The distribution of heights of binary trees and other simple trees. (English) Zbl 0795.05042

The authors derive a local limit theorem for the distribution of the number of binary trees with \(n\) interior nodes and height \(h\), when \(\delta^{-1} (\log n)^{-1/2} \leq h/2 \sqrt n \leq \delta (\log n)^{1/2}\) for fixed \(\delta>0\). They also consider the case when \(h=cn\), where \(0<c<1\), among other things. Corresponding results for more general simply generated families of trees are also given.

MSC:

05C05 Trees
05C30 Enumeration in graph theory
60F99 Limit theorems in probability theory
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References:

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