Matrix characterization of multidimensional subshifts of finite type

• Sharma, Puneet ^[1] ; Kumar, Dileep ^[1]
  1. [1] Indian Institute of Technology Jodhpur
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 20, Nº. 2, 2019, págs. 407-418
• Idioma: inglés
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• Resumen

  • 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.