Slopes of multidimensional subshifts

Abstract : In this paper we study the directions of periodicity of multidimen-sional subshifts of finite type (SFTs) and of multidimensional effectively closed and sofic subshifts. A configuration of a subshift has a slope of periodicity if it is periodic in exactly one direction, the slope representing that direction. In this paper, we prove that Σ 0 1 sets of non-commensurable Z 2 vectors are exactly the sets of slopes of 2D SFTs and that Σ 0 2 sets of non-commensurable vectors are exactly the sets of slopes of 3D SFTs, and exactly the sets of slopes of 2D and 3D sofic and effectively closed subshifts.
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Emmanuel Jeandel, Etienne Moutot, Pascal Vanier. Slopes of multidimensional subshifts. Theory of Computing Systems, Springer Verlag, In press. ⟨hal-02158012⟩

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