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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 12. Issue 1


Published on

December, 2017


Pages

27-36


DOI

https://doi.org/10.1515/udt-2017-0002

Article

Individual Gap Measures from Generalized Zeckendorf Degompositions


Authors

Robert Dorward, Pari L. Ford, Eva Fourakis, Pamela E. Harris, Steven. J. Miller, Eyvindur A. Palsson and Hannah Paugh


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.


Citation

Dorward, R., Ford, P.L.., Fourakis, E., Harris, P.E.., Miller, S.J.., Palsson, E.A.. & Paugh, H. (2017). Individual Gap Measures from Generalized Zeckendorf Degompositions. Uniform distribution theory, 12(1), 27-36. https://doi.org/10.1515/udt-2017-0002