On the variance of the Fibonacci partition function

2023/08/29 by Sam Chow, Chow, Sam, Owen Jones +1
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications

paper · pdf · doi:10.48550/arxiv.2308.15415

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.

Related

• The Dynamics of the Fibonacci Partition Function
• Convolutions Induced Discrete Probability Distributions and a New Fibonacci Constant
• Fibonacci-like property of partition function
• On Fibonacci partitions
• Fibonacci Sequence, Recurrence Relations, Discrete Probability Distributions and Linear Convolution