A simple bijection between binary trees and colored ternary trees

TL;DR

This paper introduces a straightforward bijection between binary trees and colored ternary trees, leading to a new identity involving generalized Catalan numbers, thus connecting two combinatorial structures.

Contribution

It presents a simple bijection between binary trees and colored ternary trees and derives a new combinatorial identity.

Findings

Established a bijection between binary and colored ternary trees

Derived a new identity related to generalized Catalan numbers

Connected two different combinatorial structures

Abstract

In this short note, we first present a simple bijection between binary trees and colored ternary trees and then derive a new identity related to generalized Catalan numbers.