Involutions on Tip-Augmented Plane Trees for Leaf Interchanging

TL;DR

This paper introduces two involutions on tip-augmented plane trees that interchange specific leaf types, providing bijective explanations for a question in combinatorics.

Contribution

It constructs novel involutions on tip-augmented plane trees that interchange leaf types while preserving structure, answering a previously open question.

Findings

Two involutions successfully interchange leaf types

Involutions preserve all other leaves

Provides bijective explanations for leaf interchange question

Abstract

This paper constructs two involutions on tip-augmented plane trees, as defined by Donaghey, that interchange two distinct types of leaves while preserving all other leaves. These two involutions provide bijective explanations addressing a question posed by Dong, Du, Ji, and Zhang in their work.