Subtree Size in Various Planar Trees

TL;DR

This paper derives generating functions for subtree sizes in various planar trees, enabling calculation of probabilities for subtree sizes, and demonstrates the method's applicability across different tree types.

Contribution

It introduces a unified technique using generating functions to analyze subtree size distributions in multiple types of planar trees.

Findings

Derived generating functions for subtree sizes in planar trees

Calculated probabilities of subtree sizes in different tree types

Applicable method to various tree structures

Abstract

In this paper we find the generating function for the number of vertices that have k elements in their subtree and use this generating function to calculate the probability that a vertex has a size k subtree. We also show how this same technique can be applied to calculate the probabilities for other trees and specifically apply it to 4 different types of trees.