prouet - thue - morse序列中的二进制模式

Discret. Math. Theor. Comput. Sci. Pub Date : 2019-04-15 DOI:10.46298/dmtcs.5460

J. Almeida, Ondvrej Kl'ima

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引用次数: 0

摘要

我们表明，除了单词$a^2ba^2$和$b^2ab^2$外，prouet - thue - morse序列中的所有(有限或无限)二进制模式实际上都可以在该序列中作为片段找到(直到在无限情况下交换字母)。这一结果先前归因于D. Guaiana未发表的作品，也可能来自A. Shur的出版物，仅在俄语中可用。我们还确定了(有限多)有限的二元模式，这些模式出现在非平凡的意义上，它们是通过应用一个不将序列的所有片段的集合映射到自身的自同态而获得的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Binary patterns in the Prouhet-Thue-Morse sequence

We show that, with the exception of the words $a^2ba^2$ and $b^2ab^2$, all (finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can actually be found in that sequence as segments (up to exchange of letters in the infinite case). This result was previously attributed to unpublished work by D. Guaiana and may also be derived from publications of A. Shur only available in Russian. We also identify the (finitely many) finite binary patterns that appear non trivially, in the sense that they are obtained by applying an endomorphism that does not map the set of all segments of the sequence into itself.

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Discret. Math. Theor. Comput. Sci.

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