Matrix characterization of multidimensional subshifts of finite type

Authors

  • Puneet Sharma Indian Institute of Technology Jodhpur
  • Dileep Kumar Indian Institute of Technology Jodhpur

DOI:

https://doi.org/10.4995/agt.2019.11541

Keywords:

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

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.

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Author Biographies

Puneet Sharma, Indian Institute of Technology Jodhpur

Department of Mathematics

Dileep Kumar, Indian Institute of Technology Jodhpur

Department of Mathematics

References

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Published

2019-10-01

How to Cite

[1]
P. Sharma and D. Kumar, “Matrix characterization of multidimensional subshifts of finite type”, Appl. Gen. Topol., vol. 20, no. 2, pp. 407–418, Oct. 2019.

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Articles