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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.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-00868899
Contributor : Emmanuel Jeandel Connect in order to contact the contributor
Submitted on : Wednesday, October 2, 2013 - 10:37:46 AM
Last modification on : Saturday, June 25, 2022 - 7:39:54 PM

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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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