Extensions and variations of Andrews-Merca identities

TL;DR

This paper generalizes Andrews and Merca's combinatorial interpretation of even parts in partitions into distinct parts, exploring various extensions and connections with related research.

Contribution

It introduces new variations of Andrews-Merca identities and highlights their links with recent work by Fu and Tang.

Findings

Generalized Andrews-Merca identities to broader partition classes

Established connections with Fu and Tang's research

Provided combinatorial interpretations for new partition variations

Abstract

Recently, Andrews and Merca have given a new combinatorial interpretation of the total number of even parts in all partitions of n into distinct parts. We generalise this result and consider many more variations of their work. We also highlight some connections with the work of Fu and Tang.