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Subshifts, the emptiness problem and Lovász local lemma

By Nathalie Aubrun

Appears in collection : ALEA Days / Journées ALEA

Subshifts are set of colorings of a group by a finite alphabet that respect local constraints, given by some forbidden patterns ode m. The asymmetric version of Lovász local lemma reveals particularly useful to prove the existence of a coloring inside a subshift, i.e. a coloring that avoids all the forbidden patterns. In this talk I will present some sufficient conditions on the set of forbidden patterns to get at least one coloring. Then we will see as an application why every group possesses a strongly aperiodic subshift (joint work with Sebastián Barbieri and Stéphan Thomassé).

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Citation data

  • DOI 10.24350/CIRM.V.19897403
  • Cite this video Aubrun Nathalie (3/22/22). Subshifts, the emptiness problem and Lovász local lemma. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19897403
  • URL https://dx.doi.org/10.24350/CIRM.V.19897403

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