Matrix characterization of multidimensional subshifts of finite type
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...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2019-10-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/11541 |
| _version_ | 1828826636154306560 |
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| author | Puneet Sharma Dileep Kumar |
| author_facet | Puneet Sharma Dileep Kumar |
| author_sort | Puneet Sharma |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T14:43:02Z |
| format | Article |
| id | doaj.art-478bdbbb908c4afc833fe907e0805a63 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-12T14:43:02Z |
| publishDate | 2019-10-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-478bdbbb908c4afc833fe907e0805a632022-12-22T00:21:10ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472019-10-0120240741810.4995/agt.2019.115417660Matrix characterization of multidimensional subshifts of finite typePuneet Sharma0Dileep Kumar1Indian Institute of Technology JodhpurIndian Institute of Technology JodhpurLet 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.https://polipapers.upv.es/index.php/AGT/article/view/11541multidimensional shift spacesshifts of finite typeperiodicity in multidimensional shifts of finite type |
| spellingShingle | Puneet Sharma Dileep Kumar Matrix characterization of multidimensional subshifts of finite type Applied General Topology multidimensional shift spaces shifts of finite type periodicity in multidimensional shifts of finite type |
| title | Matrix characterization of multidimensional subshifts of finite type |
| title_full | Matrix characterization of multidimensional subshifts of finite type |
| title_fullStr | Matrix characterization of multidimensional subshifts of finite type |
| title_full_unstemmed | Matrix characterization of multidimensional subshifts of finite type |
| title_short | Matrix characterization of multidimensional subshifts of finite type |
| title_sort | matrix characterization of multidimensional subshifts of finite type |
| topic | multidimensional shift spaces shifts of finite type periodicity in multidimensional shifts of finite type |
| url | https://polipapers.upv.es/index.php/AGT/article/view/11541 |
| work_keys_str_mv | AT puneetsharma matrixcharacterizationofmultidimensionalsubshiftsoffinitetype AT dileepkumar matrixcharacterizationofmultidimensionalsubshiftsoffinitetype |