Distribution of Zeckendorf expressions

Published 24 Aug 2023 in math.NT | (2308.12872v1)

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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Authors (1)

Sungkon Chang

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