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dc.contributor.authorBleak, Collin Patrick
dc.contributor.authorCameron, Peter J.
dc.contributor.authorOlukoya, Feyisayo
dc.identifier.citationBleak , C P , Cameron , P J & Olukoya , F 2021 , ' Automorphisms of shift spaces and the Higman - Thompson groups : the one-sided case ' , Discrete Analysis , vol. 2021 , 15 .
dc.identifier.otherPURE: 276067677
dc.identifier.otherPURE UUID: d1f037d4-fd02-4742-8a29-a1c0e7559ca4
dc.identifier.otherORCID: /0000-0001-5790-1940/work/100901234
dc.identifier.otherORCID: /0000-0003-3130-9505/work/100901300
dc.identifier.otherWOS: 000711079100001
dc.identifier.otherScopus: 85120722689
dc.descriptionFunding: The authors are all grateful for support from EPSRC research grant EP/R032866/1; the third author also gratefully acknowledges support from Leverhulme Trust Research Project Grant RPG-2017-159.en
dc.description.abstractLet 1 ≤ r < n be integers. We give a proof that the group Aut(Xℕn,σn) of automorphisms of the one-sided shift on n letters embeds naturally as a subgroup ℋn of the outer automorphism group Out(Gn,r) of the Higman-Thompson group Gn,r. From this, we can represent the elements of Aut(Xℕn,σn) by finite state non-initial transducers admitting a very strong synchronizing condition. Let H ∈ ℋn and write |H| for the number of states of the minimal transducer representing H. We show that H can be written as a product of at most |H| torsion elements. This result strengthens a similar result of Boyle, Franks and Kitchens, where the decomposition involves more complex torsion elements and also does not support practical a priori estimates of the length of the resulting product. We also explore the number of foldings of de Bruijn graphs and give acounting result for these for word length 2 and alphabet size n. Finally, we offer new proofs of some known results about Aut(Xℕn,σn).
dc.relation.ispartofDiscrete Analysisen
dc.rightsCopyright © 2021 The Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( 4.0/).en
dc.subjectHigman--Thompson groupsen
dc.subjectautomorphisms of the shiften
dc.subjectQA Mathematicsen
dc.titleAutomorphisms of shift spaces and the Higman - Thompson groups : the one-sided caseen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.description.statusPeer revieweden

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