Structuring multi-dimensional subshifts

Alexis Ballier 1 Emmanuel Jeandel 2
2 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : We study two relations on multi-dimensional subshifts: A pre-order based on the patterns configurations contain and the Cantor-Bendixson rank. We exhibit several structural properties of two-dimensional subshifts: We characterize the simplest aperiodic configurations in countable SFTs, we give a combinatorial characterization of uncountable subshifts, we prove that there always exists configurations without any periodicity but that have the simplest possible combinatorics in countable SFTs. Finally, we prove that some Cantor-Bendixson ranks are impossible for countable SFTs, leaving only a few unknown cases.
Type de document :
Pré-publication, Document de travail
2013
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https://hal.inria.fr/hal-00868899
Contributeur : Emmanuel Jeandel <>
Soumis le : mercredi 2 octobre 2013 - 10:37:46
Dernière modification le : jeudi 11 janvier 2018 - 06:21:25

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  • HAL Id : hal-00868899, version 1
  • ARXIV : 1309.6289

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Alexis Ballier, Emmanuel Jeandel. Structuring multi-dimensional subshifts. 2013. 〈hal-00868899〉

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