Self-Matching Properties of Beatty Sequences

Acta Polytechnica

Z. Masáková¹  E. Pelantová¹ 

关键词: Beatty sequences;    Fibonacci numbers;    cut-and-project scheme;   

DOI  :  

来源: Czech Technical University in Prague, Faculty of M

【 摘 要 】

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 G iof a generalized Fibonacci sequence almost always causes the translation of the value of the function by G i=1 . More precisely, for fixed i ϵ ℕ, we have ⌊β(j+G i )⌋ = ⌊βj⌋ + G i=1 , where j ϵ Ui. We determine the set U iof mismatches and show that it has a low frequency, namely β i .

【 授权许可】

Unknown