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Slopes of 3-dimensional Subshifts of Finite Type
Published 19 Jun 2018 in cs.DM and math.DS | (1806.07101v1)
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 angle of the periodicity vectors. In this paper, we prove that any $\Sigma0_2$ set may be realized as a a set of slopes of an SFT.
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