On the variance of the Fibonacci partition function

TL;DR

This paper investigates the variance of the Fibonacci partition function, revealing it differs from initial expectations through a proof involving diophantine systems and linear recurrences.

Contribution

It provides the first precise order of magnitude for the variance of the Fibonacci partition function, using novel mathematical techniques.

Findings

Variance order of magnitude determined

Variance differs from naive guess

Involves diophantine systems and linear recurrence

Abstract

We determine the order of magnitude of the variance of the Fibonacci partition function. The answer is different to the most naive guess. The proof involves a diophantine system and an inhomogeneous linear recurrence.