Aperiodic SFTs on Baumslag-Solitar groups

Solène J Esnay,Etienne Moutot

doi:10.1016/j.tcs.2022.03.010

Aperiodic SFTs on Baumslag-Solitar groups

Solène J Esnay, Etienne Moutot

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https://doi.org/10.1016/j.tcs.2022.03.010

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Journal: Theoretical Computer Science	Publication Date: Mar 10, 2022
Citations: 3	License type: publisher-specific-oa

Affiliation: Claude Bernard University Lyon 1, École Normale Supérieure de Lyon, French National Centre for Scientific Research, Université Toulouse III - Paul Sabatier, Toulouse Mathematics Institute, Aix-Marseille University, Institut Polytechnique de Bordeaux

#Subshifts Of Finite Type #Baumslag-Solitar Groups + Show 3 more

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Abstract

We study the periodicity of subshifts of finite type (SFT) on Baumslag-Solitar groups. We show that for residually finite Baumslag-Solitar groups there exist both strongly and weakly-but-not-strongly aperiodic SFTs. In particular, this shows that unlike Z2, but like Z3, strong and weak aperiodic SFTs are different classes of SFTs in residually finite BS groups. More precisely, we prove that a weakly aperiodic SFT on BS(m,n) due to Aubrun and Kari is, in fact, strongly aperiodic on BS(1,n); and weakly but not strongly aperiodic on any other BS(m,n). In addition, we exhibit an SFT which is weakly but not strongly aperiodic on BS(1,n); and we show that there exists a strongly aperiodic SFT on BS(n,n).

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