Warnaar's bijection and colored partition identities, II

TL;DR

This paper extends a combinatorial framework to prove new colored partition identities using a master bijection, building on previous work related to modular equations and conjectures.

Contribution

It introduces a method to combinatorially prove new colored partition identities using a unified bijection framework.

Findings

Proved several new nontrivial colored partition identities.

Extended the combinatorial framework to a broader class of identities.

Listed conjectures for further identities of similar type.

Abstract

In our previous paper, we determined a unified combinatorial framework to look at a large number of colored partition identities, and studied the five identities corresponding to the exceptional modular equations of prime degree of the Schroeter, Russell and Ramanujan type. The goal of this paper is to use the master bijection of our previous work to show combinatorially several new and highly nontrivial colored partition identities. We conclude by listing a number of further interesting identities of the same type as conjectures.