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Asymptotics for
partitions over the Fibonacci numbers and related
sequences
Michael Coons, Simon Kristensen and Mathias L. Laursen |
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Vol. 14 (2025), No. 2, 119–140
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Abstract |
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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 Fibonacci numbers, which are not necessarily distinct. This appears to be the first such asymptotic result concerning partitions over Fibonacci numbers without the restriction to distinct partitions. As well, under weak conditions, we prove analogous results for a general linear recurrences. |
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Keywords
partition, recurrence sequence, Dirichlet series
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Mathematical Subject Classification
Primary: 11P82
Secondary: 11M41
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Milestones
Received: 30 October 2024
Revised: 19 March 2025
Accepted: 4 April 2025
Published: 16 April 2025
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Authors |
| Michael Coons | |
| California State University Chico, CA United States |
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| Simon Kristensen | |
| Aarhus University Aarhus Denmark |
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| Mathias L. Laursen | |
| Aarhus University Aarhus Denmark |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
