Self-Matching Properties of Beatty Sequences
| dc.creator | Masáková, Zuzana | |
| dc.creator | Pelantová, Edita | |
| dc.date | 2006-09-22 | |
| dc.date.accessioned | 2026-07-07T07:25:07Z | |
| dc.date.available | 2026-07-07T07:25:07Z | |
| dc.description | 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 $β^i$. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0609631 | |
| dc.identifier | http://arxiv.org/abs/math/0609631 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116618 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11B39 | |
| dc.title | Self-Matching Properties of Beatty Sequences | |
| dc.type | text |