Separable Integer Partition Classes

TL;DR

This paper develops a classical partition generating function method into a versatile tool, deriving new expansions of known theorems and presenting novel results for partitions with n copies of n.

Contribution

It introduces a generalized approach to partition generating functions, expanding their applicability and providing new insights into specific partition classes.

Findings

New expansions of classical partition theorems

Results for partitions with n copies of n

Enhanced methods for partition analysis

Abstract

A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.