Asymptotics for partitions over the Fibonacci numbers and related sequences
Number Theory
2025-03-12 v3 Combinatorics
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 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.
Cite
@article{arxiv.2312.07404,
title = {Asymptotics for partitions over the Fibonacci numbers and related sequences},
author = {Michael Coons and Simon Kristensen and Mathias L. Laursen},
journal= {arXiv preprint arXiv:2312.07404},
year = {2025}
}
Comments
20 Pages. More specific asymptotics added to some proofs