Article
Individual Gap Measures from Generalized Zeckendorf Decompositions
Authors
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Abstract
Zeckendorf’s theorem states that every positive integer can be decomposed uniquely as a sum of nonconsecutive Fibonacci numbers. The distri- bution of the number of summands converges to a Gaussian, and the individual measures on gaps between summands for m € [Pn, Fn41) converge to geometric decay for almost all m as n — oo. While similar results are known for many other recurrences, previous work focused on proving Gaussianity for the number of sum- mands or the average gap measure. We derive general conditions, which are easily checked, that yield geometric decay in the individual gap measures of generalized Zeckendorf decompositions attached to many linear recurrence relations.
Keywords
Zeckendorf decompositions, individual gap measures, Lévy’s Criterion.
Citation
Dorward, R., L. Ford, P., Fourakis, E., E. Harris, P., J. Miller, S., A. Palsson, E., & Paugh, H. (2017). Individual gap measures from generalized zeckendorf decompositions. Uniform Distribution Theory, 12(1), 27–36. https://doi.org/10.1515/udt-2017-0002
R. Dorward, P. L. Ford, E. Fourakis, P. E. Harris, S. J. Miller, E. A. Palsson and H. Paugh, “Individual gap measures from generalized zeckendorf decompositions,” Uniform Distribution Theory, vol. 12, no. 1, pp. 27–36, 2017, doi: 10.1515/udt-2017-0002.
Dorward R, L. Ford P, Fourakis E, E. Harris P, J. Miller S, A. Palsson E, Paugh H. Individual gap measures from generalized zeckendorf decompositions. Uniform Distribution Theory. 2017;12(1):27–36. doi:10.1515/udt-2017-0002.
Dorward, R., L. Ford, P., Fourakis, E., E. Harris, P., J. Miller, S., A. Palsson, E. and Paugh, H. (2017), ‘Individual gap measures from generalized zeckendorf decompositions’, Uniform Distribution Theory, 12(1), pp. 27–36. Available at: https://doi.org/10.1515/udt-2017-0002.
Dorward, Robert, et al. “Individual Gap Measures from Generalized Zeckendorf Decompositions.” Uniform Distribution Theory, vol. 12, no. 1, 2017, pp. 27–36. https://doi.org/10.1515/udt-2017-0002.
Dorward, Robert, Pari L. Ford, Eva Fourakis, Pamela E. Harris, Steven. J. Miller, Eyvindur A. Palsson, and Hannah Paugh. “Individual Gap Measures from Generalized Zeckendorf Decompositions.” Uniform Distribution Theory 12, no. 1 (2017): 27–36. https://doi.org/10.1515/udt-2017-0002.
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Published by: Engineering Journals
