# Strong local rules without labels for Penrose rhombus tilings

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Time: 14:00 -- Location: LRI, 445

summary: The Penrose rhombus tilings are a subshift of tilings of the planefirst defined by R. Penrose. This subshift is crucial in the study of geometrical tilings because, though it was originally defined with 2 rhombus tiles with cuts-and-notches or arrows on the edges, it is an aperiodic subshift with local 10-fold rotational symmetry and it also is a substitution subshift and a cut-and-project subshift. We prove that the Penrose rhombus tilings can be defined by local rules without labels (the arrows or cuts-and-notches on the edges of the tiles). We present such a set of local rules. Note that the fact that there exists a set of local rules without labels is known, but we were unable to find a clear reference or an actually correct set of local rules.
Slides utilisées lors de la présentation

Category: seminars
Tags: Team seminar combinatorics