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Automorphisms of shift spaces and the Higman - Thompson groups : the one-sided case
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dc.contributor.author | Bleak, Collin Patrick | |
dc.contributor.author | Cameron, Peter J. | |
dc.contributor.author | Olukoya, Feyisayo | |
dc.date.accessioned | 2021-10-04T12:30:13Z | |
dc.date.available | 2021-10-04T12:30:13Z | |
dc.date.issued | 2021-09-20 | |
dc.identifier | 276067677 | |
dc.identifier | d1f037d4-fd02-4742-8a29-a1c0e7559ca4 | |
dc.identifier | 000711079100001 | |
dc.identifier | 85120722689 | |
dc.identifier.citation | Bleak , 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 . https://doi.org/10.19086/da.28243 | en |
dc.identifier.issn | 2397-3129 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/2004.08478v4 | |
dc.identifier.other | ORCID: /0000-0001-5790-1940/work/100901234 | |
dc.identifier.other | ORCID: /0000-0003-3130-9505/work/100901300 | |
dc.identifier.uri | https://hdl.handle.net/10023/24079 | |
dc.description | Funding: 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.abstract | Let 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.format.extent | 35 | |
dc.format.extent | 518182 | |
dc.language.iso | eng | |
dc.relation.ispartof | Discrete Analysis | en |
dc.subject | Higman--Thompson groups | en |
dc.subject | automorphisms of the shift | en |
dc.subject | Transducers | en |
dc.subject | QA Mathematics | en |
dc.subject | Mathematics(all) | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Automorphisms of shift spaces and the Higman - Thompson groups : the one-sided case | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. School of Mathematics and Statistics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Applied Mathematics | en |
dc.identifier.doi | 10.19086/da.28243 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | EP/R032866/1 | en |
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