### Admissible Reversing and Extended Symmetries for Bijective Substitutions

Bustos A, Luz D, Mañibo CN (2022)
Discrete and Computational Geometry .

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch

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Einrichtung
Abstract / Bemerkung
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 howto 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 Z(d) x H and extended symmetry group (Z(d) (sic) P) x H. A similar construction with the same symmetry group, but with extended symmetry group (Z(d) x H) (sic) P is also provided under a mild assumption on the dimension.
Stichworte
Extended symmetries; Automorphism groups; Substitution subshifts; Aperiodic tilings
Erscheinungsjahr
2022
Zeitschriftentitel
Discrete and Computational Geometry
ISSN
0179-5376
eISSN
1432-0444
Page URI
https://pub.uni-bielefeld.de/record/2963460

### Zitieren

Bustos A, Luz D, Mañibo CN. Admissible Reversing and Extended Symmetries for Bijective Substitutions. Discrete and Computational Geometry . 2022.
Bustos, A., Luz, D., & Mañibo, C. N. (2022). Admissible Reversing and Extended Symmetries for Bijective Substitutions. Discrete and Computational Geometry . https://doi.org/10.1007/s00454-022-00387-8
Bustos, A., Luz, D., and Mañibo, C. N. (2022). Admissible Reversing and Extended Symmetries for Bijective Substitutions. Discrete and Computational Geometry .
Bustos, A., Luz, D., & Mañibo, C.N., 2022. Admissible Reversing and Extended Symmetries for Bijective Substitutions. Discrete and Computational Geometry .
A. Bustos, D. Luz, and C.N. Mañibo, “Admissible Reversing and Extended Symmetries for Bijective Substitutions”, Discrete and Computational Geometry , 2022.
Bustos, A., Luz, D., Mañibo, C.N.: Admissible Reversing and Extended Symmetries for Bijective Substitutions. Discrete and Computational Geometry . (2022).
Bustos, Alvaro, Luz, Daniel, and Mañibo, Chrizaldy Neil. “Admissible Reversing and Extended Symmetries for Bijective Substitutions”. Discrete and Computational Geometry (2022).

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