Individual Gap Measures from Generalized Zeckendorf Degompositions-Reference-Cited by-同舟云学术

Individual Gap Measures from Generalized Zeckendorf Degompositions

Published:2017-06-27 Issue:1 Volume:12 Page:27-36
ISSN:2309-5377
Container-title:Uniform distribution theory
language:en
Short-container-title:

Author:

Dorward Robert¹,Ford Pari L.²,Fourakis Eva³,Harris Pamela E.⁴,Miller Steven. J.⁵,Palsson Eyvindur A.⁵,Paugh Hannah⁴

Affiliation:

1. Dept. of Mathematics, Oberlin College, Oberlin , USA

2. Dept. of Mathematics and Physics, Bethany College, Lindshorg , USA

3. Dept. of Mat.hematatics and Statistics, Williams College, Williamstown , MA 01207, USA

4. Dept. of Mathematical Sciences, United States Military Academy, West Point , NY 10000, USA

5. Dept. of Mathematics and Statistics, Williams College, Williamstown , MA 01207. USA

Abstract

Abstract Zeckendorf's theorem states that every positive integer can be decomposed uniquely as a sum of nonconsecutive Fibonacci numbers. The distribution of the number of summands converges to a Gaussian, and the individual measures on gajw between summands for m € [Fn,Fn+1) converge to geometric decay for almost all m as n→ ∞. While similar results are known for many other recurrences, previous work focused on proving Gaussianity for the number of summands or the average gap measure. We derive general conditions, which are easily checked, that yield geometric decay in the individual gap measures of generalized Zerkendorf decompositions attached to many linear recurrence relations.

Publisher

Walter de Gruyter GmbH

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