Self-Matching Properties of Beatty Sequences

Authors

  • Z. Masáková
  • E. Pelantová

DOI:

https://doi.org/10.14311/924

Keywords:

Beatty sequences, Fibonacci numbers, cut-and-project scheme

Abstract

We study the selfmatching properties of Beatty sequences, in particular of the graph of the function  ⌊ jβ ⌋ against j for every quadratic unit βϵ (0,1). We show that translation in the argument by an element Gi of a generalized Fibonacci sequence almost always causes the translation of the value of the function by Gi=1. More precisely, for fixed i ϵ ℕ, we have ⌊β(j+Gi)⌋ = ⌊βj⌋ + Gi=1, where j ϵ Ui. We determine the set Ui of mismatches and show that it has a low frequency, namely βi.

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Published

2007-01-02

Issue

Vol. 47 No. 2-3 (2007)

Section

Articles

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How to Cite

Masáková, Z., & Pelantová, E. (2007). Self-Matching Properties of Beatty Sequences. Acta Polytechnica, 47(2-3). https://doi.org/10.14311/924