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2019 Bin decompositions
Daniel Gotshall, Pamela E. Harris, Dawn Nelson, Maria D. Vega, Cameron Voigt
Involve 12(3): 503-519 (2019). DOI: 10.2140/involve.2019.12.503

Abstract

It is well known that every positive integer can be expressed as a sum of nonconsecutive Fibonacci numbers provided the Fibonacci numbers satisfy F n = F n 1 + F n 2 for n 3 , F 1 = 1 and F 2 = 2 . For any n , m we create a sequence called the ( n , m ) -bin sequence with which we can define a notion of a legal decomposition for every positive integer. These sequences are not always positive linear recurrences, which have been studied in the literature, yet we prove, that like positive linear recurrences, these decompositions exist and are unique. Moreover, our main result proves that the distribution of the number of summands used in the ( n , m ) -bin legal decompositions displays Gaussian behavior.

Citation

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Daniel Gotshall. Pamela E. Harris. Dawn Nelson. Maria D. Vega. Cameron Voigt. "Bin decompositions." Involve 12 (3) 503 - 519, 2019. https://doi.org/10.2140/involve.2019.12.503

Information

Received: 18 April 2018; Revised: 10 July 2018; Accepted: 22 July 2018; Published: 2019
First available in Project Euclid: 5 February 2019

zbMATH: 07033145
MathSciNet: MR3905344
Digital Object Identifier: 10.2140/involve.2019.12.503

Subjects:
Primary: 11B39, 60B10, ‎65Q30

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 3 • 2019
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