The sum of digits functions of the Zeckendorf and the base phi expansions

Journal article (2021)

Authors

F.M. Dekking Applied Probability - EEMCS
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2021 F.M. Dekking
DOI
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https://doi.org/10.1016/j.tcs.2021.01.011
Base phi Fibonacci word Generalized Beatty sequence Wythoff sequence Zeckendorf expansion
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Published Date

2021

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

We consider the sum of digits functions for both base phi, and for the Zeckendorf expansion of the natural numbers. For both sum of digits functions we present morphisms on infinite alphabets such that these functions viewed as infinite words are letter-to-letter projections of fixed points of these morphisms. We characterize the first differences of both functions a) with generalized Beatty sequences, or unions of generalized Beatty sequences, and b) with morphic sequences.