On the Average Shape of Binary Trees

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1980 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Algebraic Discrete Methods, volume 1, pages 43-50 (issn: 0196-5212, eissn: 2168-345X,

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Authors: Frank Ruskey;

doi: 10.1137/0601007

On the Average Shape of Binary Trees

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Abstract

The average level numbers of the leaves of a binary tree are studied, where each binary tree is regarded as being equally likely. A formula is derived for the number of binary trees with jth leaf at a prescribed level. The asymptotic behavior of the average level number of the jth leaf is determined. The average level numbers are shown to first increase and then decrease.

Keywords

Graph theory (including graph drawing) in computer science, asymptotic behavior, average level numbers of the leaves of a binary tree, Trees

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