Automorphisms of $\mathcal{B}$-free and other Toeplitz shifts

TL;DR

This paper investigates the automorphism groups of regular Toeplitz subshifts, especially $ ext{B}$-free systems, providing conditions for triviality and examples with complex automorphism structures.

Contribution

It offers new sufficient conditions for trivial automorphism groups and constructs examples with automorphisms of arbitrarily large finite order.

Findings

Conditions for trivial automorphism groups in $ ext{B}$-free Toeplitz subshifts

Existence of $ ext{B}$-free Toeplitz subshifts with automorphisms of large finite order

Extension of previous results on automorphism groups of Toeplitz systems

Abstract

We present sufficient conditions for the triviality of the automorphism group of regular Toeplitz subshifts and give a broad class of examples from the class of $\mathcal{B}$-free subshifts satisfying them, extending [10]. On the other hand we provide an example of a $\mathcal{B}$-free Toeplitz subshift whose automorphism group has elements of arbitrarily large finite order, answering Question 11 in [13].