The Fractal and The Recurrence Equations Concerning The Integer Partitions

TL;DR

This paper introduces a fractal-based approach to counting integer partitions and derives related recurrence equations, including the pentagonal number theorem, offering a novel mathematical perspective.

Contribution

It presents a new fractal method for analyzing integer partitions and deduces recurrence equations like the pentagonal number theorem.

Findings

Fractal method effectively counts integer partitions.

Recurrence equations such as the pentagonal number theorem are derived.

Provides a new mathematical framework for partition analysis.

Abstract

This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the pentagonal number theorem.