Harmonic Partitions of Positive Integers and Bosonic Extension of Euler's Pentagonal Number Theorem

TL;DR

This paper offers a cohomological derivation of Euler's Pentagonal Number Theorem and introduces a bosonic extension, providing new insights into classical number theory through algebraic methods.

Contribution

It presents a novel cohomological approach to derive Euler's theorem and establishes a new bosonic extension, expanding the theorem's theoretical framework.

Findings

Cohomological derivation of Euler's Pentagonal Number Theorem

New bosonic extension of the theorem

Re-derivation of Euler's identity using cohomology

Abstract

In this paper, we first propose a cohomological derivation of the celebrated Euler's Pentagonal Number Theorem. Then we prove an identity that corresponds to a bosonic extension of the theorem. The proof corresponds to a cohomological re-derivation of Euler's another celebrated identity.