On The Joint Normality of Certain Statistics on Ordered Trees

TL;DR

This paper develops Maple algorithms to analyze the distribution of vertices with specific children counts in ordered trees, providing experimental evidence for their joint asymptotic normality through moment calculations.

Contribution

It introduces algorithms for studying vertex degree distributions in ordered trees and demonstrates their asymptotic normality through experimental analysis.

Findings

Vertices with specific children counts are pairwise asymptotically normal.

The Maple package effectively computes mixed moments for these statistics.

Experimental results support the normality hypothesis.

Abstract

We develop algorithms, implemented in Maple, that study the number of vertices with a particular number of children in a random ordered tree where all vertices must have a number of children in some finite set. By calculating the mixed moments of two such numbers, the package gives strong experimental evidence numbers are pairwise asymptotically normal.