Computing automorphism groups of shifts using atypical equivalence classes
Computing automorphism groups of shifts using atypical equivalence classes
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使用非典型等价类计算移位的自同构群
DOI：
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发表时间：
2023
期刊：
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通讯作者：
R. Yassawi
中科院分区：
文献类型：
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作者：
R. Yassawi
研究了一个无限极小位移（X,σ）的自同构群，使得复杂度差函数p(n+1)−p(n)有界。给出了Aut(X,σ)/ < σ >的一些新的界，并研究了单侧情况。对于一类Toeplitz位移，包括高度为1的等长原元替换定义的位移，证明了其双侧自同构群是一个循环群。接下来，我们将重点讨论由原语恒长替换产生的移位。对于这些移位，我们给出了一个计算它们的双边自同构群的算法。最后，我们证明了使用相同的技术，我们能够计算两个这样的位移之间的共轭集。
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 Aut(X ,σ)/〈σ〉 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. Finally we show that with the same techniques, we are able to compute the set of conjugacies between two such shifts.