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dc.contributor.authorBleak, Collin
dc.contributor.authorOlukoya, Feyishayo
dc.date.accessioned2023-07-07T16:30:09Z
dc.date.available2023-07-07T16:30:09Z
dc.date.issued2023-01-31
dc.identifier.citationBleak , C & Olukoya , F 2023 ' Conjugacy for certain automorphisms of the one-sided shift via transducers ' arXiv . https://doi.org/10.48550/arXiv.2301.13570en
dc.identifier.otherPURE: 283530532
dc.identifier.otherPURE UUID: 0bb5c48f-0638-4d5d-b88d-564d0cc43019
dc.identifier.otherArXiv: http://arxiv.org/abs/2301.13570v1
dc.identifier.urihttps://hdl.handle.net/10023/27920
dc.description53 Pages, 12 figuresen
dc.description.abstractWe address the following open problem, implicit in the 1990 article "Automorphisms of one-sided subshifts of finite type" of Boyle, Franks and Kitchens (BFK): "Does there exists an element $\psi$ in the group of automorphisms of the one-sided shift $\operatorname{Aut}(\{0,1,\ldots,n-1\}^{\mathbb{N}}, \sigma_{n})$ so that all points of $\{0,1,\ldots,n-1\}^{\mathbb{N}}$ have orbits of length $n$ under $\psi$ and $\psi$ is not conjugate to a permutation?" Here, by a 'permutation' we mean an automorphism of one-sided shift dynamical system induced by a permutation of the symbol set $\{0,1,\ldots,n-1\}$. We resolve this question by showing that any $\psi$ with properties as above must be conjugate to a permutation. Our techniques naturally extend those of BFK using the strongly synchronizing automata technology developed here and in several articles of the authors and collaborators (although, this article has been written to be largely self-contained).
dc.format.extent53
dc.language.isound
dc.publisherarXiv
dc.rights(c) 2023 the authors. This open access preprint is available under a Creative Commons Attribution licenceen
dc.subjectmath.GRen
dc.subjectcs.FLen
dc.subjectmath.DSen
dc.subject54H15, 28D15, 22F50, 68Q99en
dc.subjectQA Mathematicsen
dc.subject.lccQAen
dc.titleConjugacy for certain automorphisms of the one-sided shift via transducersen
dc.typePreprinten
dc.description.versionPreprinten
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.48550/arXiv.2301.13570
dc.identifier.urlhttps://arxiv.org/abs/2301.13570en


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