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Slopes of multidimensional subshifts. (English) Zbl 1440.37025
Summary: In this paper we study the directions of periodicity of multidimensional 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 \({{\Sigma }^0_1}\) sets of non-commensurable \(\mathbb{Z}^2\) vectors are exactly the sets of slopes of 2D SFTs and that \({{\Sigma }^0_2}\) 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.
37B51 Multidimensional shifts of finite type
37B10 Symbolic dynamics
Full Text: DOI
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