Matrix characterization of multidimensional subshifts of finite type

Puneet Sharma, Dileep Kumar

Abstract

Let X ⊂ AZd be a 2-dimensional subshift of finite type. We prove that any 2-dimensional subshift of finite type can be characterized by a square matrix of infinite dimension. We extend our result to a general d-dimensional case. We prove that the multidimensional shift space is non-empty if and only if the matrix obtained is of positive dimension. In the process, we give an alternative view of the necessary and sufficient conditions obtained for the non-emptiness of the multidimensional shift space. We also give sufficient conditions for the shift space X to exhibit periodic points.


Keywords

multidimensional shift spaces; shifts of finite type; periodicity in multidimensional shifts of finite type

Subject classification

37B10; 37B20; 37B50.

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References

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