Torsion-free S-adic shifts and their spectrum
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Editors
Lemanczyk, M
Publisher
DOI
10.4064/sm221028-6-5
Journal
Studia Mathematica
ISSN
1730-6337
Metadata
Show full item recordAbstract
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.
Authors
Yassawi, RCollections
- Mathematics [1468]