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arXiv · 2606.27170

On automorphisms of $\mathscr{B}$-admissible and related subshifts

Aurelia Dymek·Nazrul Haque·Stanisław Kasjan
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Abstract

We adapt ideas of Kim and Roush [15], originally developed in the study of automorphisms of sofic subshifts, to obtain sufficient conditions under which a subshift has a huge automorphism group. We apply this approach to non-sofic subshifts defined by sets of multiples. In particular, we establish a dichotomy for the $\mathscr{B}$-admissible subshift: its automorphism group is either trivial or contains an embedded copy of the automorphism group of the full shift $\{0,1\}^{\mathbb Z}$. In the latter case, we say that the automorphism group is huge. We further show that the automorphism group of the hereditary closure of the $\mathscr{B}$-free subshift is huge whenever $\mathscr{B}\subset \mathbb N$ is infinite and contains no infinite pairwise coprime subset.

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Aurelia Dymek, Nazrul Haque, Stanisław Kasjan. 2026-06-25. On automorphisms of $\mathscr{B}$-admissible and related subshifts. https://arxiv.org/abs/2606.27170

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