A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Torsion-free $S$-adic shifts and their spectrum

Volume 272 / 2023

Álvaro Bustos-Gajardo, Neil Mañibo, Reem Yassawi Studia Mathematica 272 (2023), 159-198 MSC: Primary 37B10; Secondary 37B52, 37A05. DOI: 10.4064/sm221028-6-5 Published online: 4 September 2023

Abstract

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-recognisability, which can be used as a substitute for recognisability. Indeed quasi-recognisable 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

  • Álvaro Bustos-GajardoSchool of Mathematics and Statistics
    The Open University
    Milton Keynes, MK7 6AA, UK
    and
    Facultad de Matemáticas Pontificia Universidad Católica de Chile
    4860 Macul, Santiago, Chile
    e-mail
  • Neil MañiboSchool of Mathematics and Statistics
    The Open University
    Milton Keynes, MK7 6AA, UK
    and
    Faculty of Mathematics
    Bielefeld University
    33501, Bielefeld, Germany
    e-mail
  • Reem YassawiSchool of Mathematics and Statistics
    The Open University
    Milton Keynes, MK7 6AA, UK
    and
    School of Mathematical Sciences
    Queen Mary University of London
    London, E1 4NS, UK
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image