Andrews Style Partition Identities

TL;DR

This paper introduces a method to generate multiple partition identities simultaneously, generalizing Andrews' results across all moduli by solving functional equations for generating functions.

Contribution

The paper presents a novel approach that constructs solutions to functional equations, enabling the derivation of a broad class of partition identities in a unified framework.

Findings

Successfully generalizes Andrews' partition identities to all moduli

Provides a new method for solving functional equations related to generating functions

Achieves a unified construction of partition identities

Abstract

We propose a method to construct a variety of partition identities at once. The main application is an all-moduli generalization of some of Andrews' results in [5]. The novelty is that the method constructs solutions to functional equations which are satisfied by the generating functions. In contrast, the conventional approach is to show that a variant of well-known series satisfies the system of functional equations, thus reconciling two separate lines of computations.