Torsion-free $S$-adic shifts and their spectrum
Torsion-free $S$-adic shifts and their spectrum
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DOI：
10.4064/sm221028-6-5
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发表时间：
2022-09
影响因子：
0.8
通讯作者：
'Alvaro Bustos-Gajardo;Neil Mañibo;R. Yassawi
中科院分区：
文献类型：
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作者：
'Alvaro Bustos-Gajardo;Neil Mañibo;R. Yassawi
在这项工作中，我们研究$S$-进移位产生的序列是恒定长度的态射。我们称一个等长态射序列是无挠的，如果其中一个长度的任何素因子是无穷多个长度的因子。我们证明了无挠方向序列产生的移位具有准可识别性，它可以作为可识别性的替代。事实上，准可识别的方向序列可以被可识别的方向序列代替。有了这个，我们给出了一个更精细的描述的频谱上定义的一个序列的字母表的大小有界的无扭序列所产生的移位，在高度和列数的概念的扩展。我们用例子说明我们的结果，解释可能出现的微妙之处。
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.