Counting edges according to edge-type in $t$-ary trees

TL;DR

This paper applies the Lagrange inversion formula to enumerate $t$-ary trees based on edge types, providing a detailed combinatorial analysis of their structure.

Contribution

It introduces a novel enumeration method for $t$-ary trees considering edge types using the Lagrange inversion formula.

Findings

Derived explicit formulas for counting edges by type in $t$-ary trees

Extended enumeration techniques to various edge classifications

Enhanced understanding of $t$-ary tree structures

Abstract

Using the Lagrange inversion formula, $t$-ary trees are enumerated with respect to edge type (left, middle, right for ternary trees).