Distribution of Zeckendorf expressions

Sungkon Chang

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arXiv · 2308.12872

Distribution of Zeckendorf expressions

Sungkon Chang

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Abstract

By Zeckendorf's Theorem, every positive integer is uniquely written as a sum of distinct non-adjacent Fibonacci terms. In this paper, we investigate the asymptotic formula of the number of binary expansions $<x$ that have no adjacent terms, and generalize the result to the setting of general linear recurrences with non-negative integer coefficients.

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Sungkon Chang. 2023-08-24. Distribution of Zeckendorf expressions. https://arxiv.org/abs/2308.12872

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