Admissible reversing and extended symmetries for bijective substitutions

2021/01/26 by Bustos, Álvaro, Luz, Daniel, Mañibo, Neil · 1 citation
#20B27 #37B10 #37B52 #52C23 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2101.10988

Abstract

In this paper, we deal with reversing and extended symmetries of shifts generated by bijective substitutions. We provide equivalent conditions for a permutation on the alphabet to generate a reversing/extended symmetry, and algorithms how to check them. Moreover, we show that, for any finite group G and any subgroup P of the d-dimensional hyperoctahedral group, there is a bijective substitution which generates an aperiodic hull with symmetry group ℤ^d× G and extended symmetry group (ℤ^d \rtimes P)× G.

Cited by

• Radius-zero Extended Symmetries and Irregular Fibres of ℤ^d-Substitution Subshifts

Related

• Computation of extended symmetry groups for multidimensional subshifts with hierarchical structure
• Radius-zero Extended Symmetries and Irregular Fibres of ℤ^d-Substitution Subshifts
• Symmetries and reversing symmetries of trace maps
• Reversing Symmetry Groups of Cat Maps
• Almost automorphic and bijective factors of substitution shifts