Slopes of 3-dimensional Subshifts of Finite Type

Abstract : In this paper we study the directions of periodicity of three-dimensional subshifts of finite type (SFTs) and in particular their slopes. A configuration of a subshift has a slope of periodicity if it is periodic in exactly one direction, the slope being the angles of the periodicity vector. In this paper, we prove that any Σ_2 set may be realized as a a set of slopes of an SFT.
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Etienne Moutot, Pascal Vanier. Slopes of 3-dimensional Subshifts of Finite Type. CSR 2018, Jun 2018, Moscou, Russia. pp.257--268, ⟨10.1007/978-3-319-90530-3_22⟩. ⟨hal-01772574⟩

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