Bijective Proofs of Identities from Colored Binary Trees

TL;DR

This paper presents bijective proofs for two combinatorial identities involving generalized Catalan numbers, offering new combinatorial insights into these mathematical formulas.

Contribution

It introduces bijective proofs for identities related to generalized Catalan numbers, expanding understanding of combinatorial structures.

Findings

Bijective proofs established for two identities involving generalized Catalan numbers.

Enhanced combinatorial understanding of identities proposed by Sun.

New methods for proving identities in combinatorics using bijections.

Abstract

This note provide bijective proofs of two combinatorial identities involving generalized Catalan number $C_{m,5}(n)={m\over 5n+m}{5n+m\choose n}$ recently proposed by Sun.