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Article Dans Une Revue Theoretical Computer Science Année : 2019

Nivat's conjecture and pattern complexity in algebraic subshifts

Résumé

We study Nivat's conjecture on algebraic subshifts and prove that in some of them every low complexity configuration is periodic. This is the case in the Ledrappier subshift (the 3-dot system) and, more generally, in all two-dimensional algebraic subshifts over Fp defined by a polynomial without line polynomial factors in more than one direction. We also find an algebraic subshift that is defined by a product of two line polynomials that has this property (the 4-dot system) and another one that does not.
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hal-02130713 , version 1 (16-05-2019)

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Jarkko Kari, Etienne Moutot. Nivat's conjecture and pattern complexity in algebraic subshifts. Theoretical Computer Science, 2019, ⟨10.1016/j.tcs.2018.12.029⟩. ⟨hal-02130713⟩
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