2-colored Rogers-Ramanujan partition identities

TL;DR

This paper introduces 2-colored Rogers-Ramanujan partitions by combining partition types, deriving identities through functional equations, and establishing connections with overpartition identities and colored partitions.

Contribution

It presents a novel concept of 2-colored Rogers-Ramanujan partitions and provides new identities and correspondences with overpartitions.

Findings

Derived new identities for 2-colored Rogers-Ramanujan partitions

Established a correspondence between colored partitions and overpartitions

Found that some overpartition identities coincide with the new findings

Abstract

In this paper, we combined two types of partitions and introduced 2-colored Rogers-Ramanujan partitions. By finding some functional equations and using a constructive method, some identities have been found. Some Overpartition identities coincide with our findings. A correspondence between colored partitions and overpartitions is provided.