Combinatorial proof of an identity of Andrews and Yee

TL;DR

This paper provides a combinatorial proof of a specific identity related to partition functions, expanding understanding of identities studied by Andrews and Yee involving two-variable generalizations.

Contribution

The paper introduces a new combinatorial proof for an identity involving partition functions, complementing prior analytical approaches by Andrews and Yee.

Findings

Established a combinatorial proof for the identity

Enhanced understanding of partition function identities

Connected two-variable generalizations to combinatorial structures

Abstract

Recently, Andrews and Yee studied two-variable generalizations of two identities involving partition functions $p_\omega(n)$ and $p_\nu(n)$ introduced by Andrews, Dixit and Yee. In this paper, we present a combinatorial proof of an interesting identity in their work.