PARTITION THEORY ( A RECURSIVE APPROACH)

Abstract

This research paper investigates integer partitions and introduces a new formula for calculating the number of partitions of a number. The formula is developed through mathematical reasoning and explored using examples and properties of integer partitions. It also introduces new terminology for some concepts related to it like Max part, defined precisely to describe the structures studied. The paper covers motivation, definitions, derivation, examples, and observations, and discusses connections to partition theory and combinatorics. The results form an original investigation that may support further study.