Self-Matching Properties of Beatty Sequences

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We study the selfmatching properties of Beatty sequences, in particular of the graph of the function $\lfloor jβ\rfloor $ against $j$ for every quadratic unit $β\in(0,1)$. We show that translation in the argument by an element $G_i$ of generalized Fibonacci sequence causes almost always the translation of the value of function by $G_{i-1}$. More precisely, for fixed $i\in\N$, we have $\bigl\lfloor β(j+G_i)\bigr\rfloor = \lfloor βj\rfloor +G_{i-1}$, where $j\notin U_i$. We determine the set $U_i$ of mismatches and show that it has a low frequency, namely $β^i$.
7 pages

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Combinatorics, Number Theory, 11B39

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http://salesiana.dossiersoluciones.com/handle/123456789/116618

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0609631
 http://arxiv.org/abs/math/0609631

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arXiv