Asymptotics for partitions over the Fibonacci numbers and related sequences

2023/12/12 by Michael James Coons, Coons, Michael, Simon Kristensen +3
Mathematics · #11M41 #11P82 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2312.07404

openalex publication_date 2023/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, harkening back to ideas of Hardy and Ramanujan, Mahler and de Bruijn, with the addition of more recent results on the Fibonacci Dirichlet series, we determine the asymptotic number of ways p_F(n) to write an integer as the sum of non-distinct Fibonacci numbers. This appears to be the first such asymptotic result concerning non-distinct partitions over Fibonacci numbers. As well, under weak conditions, we prove analogous results for a general linear recurrences.

Related

• On Zeckendorf Related Partitions Using the Lucas Sequence
• On the sum of a prime and two Fibonacci numbers
• On Fibonacci partitions
• A note on the power sums of the number of Fibonacci partitions
• Difference in the Number of Summands in the Zeckendorf Partitions of Consecutive Integers