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arXiv · 1505.02482

Computing automorphism groups of shifts using atypical equivalence classes

Ethan M. Coven·Anthony Quas·Reem Yassawi
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Abstract

We study the automorphism group of an infinite minimal shift $(X,σ)$ such that the complexity difference function, $p(n+1)-p(n)$, is bounded. We give some new bounds on $\mbox{Aut}(X,σ)/\langle σ\rangle$ and also study the one-sided case. For a class of Toeplitz shifts, including the class of shifts defined by constant length primitive substitutions with a coincidence and with height one, we show that the two-sided automorphism group is a cyclic group. We next focus on shifts generated by primitive constant length substitutions. For these shifts, we give an algorithm that computes their two-sided automorphism group, As a corollary we describe how to compute the set of conjugacies between two such shifts.

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Ethan M. Coven, Anthony Quas, Reem Yassawi. 2017-02-01. Computing automorphism groups of shifts using atypical equivalence classes. https://arxiv.org/abs/1505.02482

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