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Admissible Reversing and Extended Symmetries for Bijective Substitutions

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Bibliographic Details
Main Authors: Álvaro, Bustos, Daniel, Luz, Neil, Mañibo
Format: Book
Language:English
Published: Springer 2023
Subjects:
group Zd×H
group (Zd⋊P)×H
Online Access:https://link.springer.com/article/10.1007/s00454-022-00387-8
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7426
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spelling oai:localhost:PNK-74262023-04-03T04:03:44Z Admissible Reversing and Extended Symmetries for Bijective Substitutions Álvaro, Bustos Daniel, Luz Neil, Mañibo group Zd×H group (Zd⋊P)×H CC BY In this paper, we deal with reversing and extended symmetries of subshifts generated by bijective substitutions. We survey some general algebraic and dynamical properties of these subshifts and recall known results regarding their symmetry groups. We provide equivalent conditions for a permutation on the alphabet to generate a reversing/extended symmetry, and algorithms how to compute them. Moreover, for any finite group H and any subgroup P of the d-dimensional hyperoctahedral group, we construct a bijective substitution which generates an aperiodic subshift with symmetry group Zd×H and extended symmetry group (Zd⋊P)×H. A similar construction with the same symmetry group, but with extended symmetry group (Zd×H)⋊P is also provided under a mild assumption on the dimension. 2023-04-03T04:03:44Z 2023-04-03T04:03:44Z 2022 Book https://link.springer.com/article/10.1007/s00454-022-00387-8 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7426 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic group Zd×H
group (Zd⋊P)×H
spellingShingle group Zd×H
group (Zd⋊P)×H
Álvaro, Bustos
Daniel, Luz
Neil, Mañibo
Admissible Reversing and Extended Symmetries for Bijective Substitutions
description CC BY
format Book
author Álvaro, Bustos
Daniel, Luz
Neil, Mañibo
author_facet Álvaro, Bustos
Daniel, Luz
Neil, Mañibo
author_sort Álvaro, Bustos
title Admissible Reversing and Extended Symmetries for Bijective Substitutions
title_short Admissible Reversing and Extended Symmetries for Bijective Substitutions
title_full Admissible Reversing and Extended Symmetries for Bijective Substitutions
title_fullStr Admissible Reversing and Extended Symmetries for Bijective Substitutions
title_full_unstemmed Admissible Reversing and Extended Symmetries for Bijective Substitutions
title_sort admissible reversing and extended symmetries for bijective substitutions
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s00454-022-00387-8
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7426
_version_ 1762184302708129792
score 8.891053

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