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arXiv · 2302.06258

Recognizability in S-adic shifts

Marie-Pierre Béal·Dominique Perrin·Antonio Restivo·Wolfgang Steiner
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Abstract

We investigate questions related to the notion of recognizability of sequences of morphisms, a generalization of Moss{\'e}'s Theorem. We consider the most general class of morphisms including ones with erasable letters. The main result states that a sequence of morphisms with finite alphabet rank is eventually recognizable for aperiodic points, improving and simplifying a result of Berth{\'e} et al. (2019). This also provides a new simple proof for the recognizability of a single morphism on its shift space. The main ingredient of the proof are elementary morphisms.

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Marie-Pierre Béal, Dominique Perrin, Antonio Restivo, Wolfgang Steiner. 2023-02-13. Recognizability in S-adic shifts. https://arxiv.org/abs/2302.06258

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