Counting paths in perfect trees

TL;DR

This paper derives exact formulas for counting paths of specific lengths in perfect m-ary trees, both rooted and unrooted, extending previous binary tree results.

Contribution

It provides new exact expressions for path counts in perfect m-ary trees, generalizing known binary tree formulas to broader tree structures.

Findings

Exact path count formulas for rooted perfect m-ary trees

Extension of path counting to unrooted perfect m-ary trees

Generalization of binary tree results to m-ary trees

Abstract

We present some exact expressions for the number of paths of a given length in a perfect $m$-ary tree. We first count the paths in perfect rooted $m$-ary trees and then use the results to determine the number of paths in perfect unrooted $m$-ary trees, extending a known result for binary trees.