Segments on the Right Branch of a Binary Tree

TL;DR

This paper proves that as binary trees grow large, the average number of segments on their right branch approaches three, and the distribution of such segments converges to a specific probability distribution.

Contribution

It establishes asymptotic results for the distribution and average number of segments on the right branch of binary trees, providing new insights into their structural properties.

Findings

Average number of right-branch segments tends to 3 as tree size increases

Distribution of right-branch segments converges to k/2^{k+1}

Results hold for large binary trees with size n

Abstract

It is proved that the average number of segments on the right branch of a binary tree of size n tends to 3 as n tends to $\infty$. Also the fraction of trees with k segments on the right branch from all trees of size n tends to $\frac{k}{2^{k+1}}$ as n tends to $\infty$