论文标题
无扭转的$ S $ - adic换班及其频谱
Torsion-free $S$-adic shifts and their spectrum
论文作者
论文摘要
在这项工作中，我们研究了由恒定长度的形态序列产生的$ s $ addic变化。如果一个长度之一是无限的许多长度的分裂，我们称之为无扭转的恒定形态的序列无扭转。我们表明，无扭转的指示序列会产生享受准识别性的特性的变化，可以用作替代识别性。实际上，准识别的指令序列可以用可识别的指令序列代替。这样，我们就通过在高度和列数的概念的扩展方面，对由有界大小的字母序列定义的无扭转序列生成的移位频谱进行了更精细的描述。我们在整个过程中以解释可能出现的微妙之处的示例来说明我们的结果。
In this work we study $S$-adic shifts generated by sequences of morphisms that are constant-length. We call a sequence of constant-length morphisms torsion-free if any prime divisor of one of the lengths is a divisor of infinitely many of the lengths. We show that torsion-free directive sequences generate shifts that enjoy the property of quasi-recognizability which can be used as a substitute for recognizability. Indeed quasi-recognizable directive sequences can be replaced by a recognizable directive sequence. With this, we give a finer description of the spectrum of shifts generated by torsion-free sequences defined on a sequence of alphabets of bounded size, in terms of extensions of the notions of height and column number. We illustrate our results throughout with examples that explain the subtleties that can arise.
