Horton-Strahler numbers for binary butterfly trees: exact analysis

TL;DR

This paper provides an exact combinatorial analysis of Horton-Strahler numbers for binary butterfly trees, revealing asymptotic similarities to classical binary trees despite their unique construction.

Contribution

It introduces a detailed combinatorial approach to analyze Horton-Strahler numbers in binary butterfly trees, extending understanding of their probabilistic structure.

Findings

Asymptotic results match those of classical binary trees

Exact combinatorial formulas derived for Horton-Strahler numbers

Binary butterfly trees exhibit similar Horton-Strahler number distribution asymptotically

Abstract

Peca suggested in a recent paper on the arxiv to consider binary butterfly trees and their Horton-Strahler numbers. The trees are obtained by glueing two binary trees together in a special way; the results are again binary trees but with a different probability distribution. A thorough combinatorial analysis is provided and leads asymptotically to the same results as for classical binary trees.