Combinatorial proofs of several partition identities of Andrews and Merca

TL;DR

This paper provides combinatorial proofs for multiple partition identities originally proposed by Andrews and Merca, using a bijection by Fu and Tang, and extends one identity with new partition weights.

Contribution

It introduces combinatorial proofs for several identities and extends one identity by incorporating two new partition weights.

Findings

Successfully proved multiple partition identities combinatorially.

Extended an identity by introducing two weights for partitions.

Enhanced understanding of partition identities through bijective methods.

Abstract

Based on a bijection due to Fu and Tang, we provide combinatorial proofs of several partition identities of Andrews and Merca. We also introduce two weights for partitions to extend one of these identities.