On self-matching within integer part sequences
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- 作者：Keith Tognetti
- 关键词：Self matching ; Characteristic ; Sturmian ; Bernoulli ; Integer parts ; Moiré ; Sequence
- 刊名：Discrete Mathematics
- 出版年：2008
- 出版时间：28 December 2008
- 年：2008
- 卷：308
- 期：24
- 页码：6539-6545
- 全文大小：681 K
文摘
With α irrational the graph of [jα] against integer j, displays interesting patterns of self-matching. This is best seen by comparing the Bernoulli (characteristic Sturmian) or difference sequence βj, term by term with the Bernoulli sequence displaced by k terms βj−k, where βj=[(j+1)α]−[jα].
It is shown that the fraction of such self-matching is the surprisingly simple Of particular interest is the graph of M(k) against k as it is seen to exhibit an unexpected Moiré pattern obtained simply by folding the lower half of the graph of {kα} over the upper half.