Title

An application of topological multiple recurrence to tiling

Abstract

We show that given any tiling of Euclidean space, any geometric pattern of points, we can find a patch of tiles (of arbitrarily large size) so that copies of this patch appear in the tiling nearly centered on a scaled and translated version of the pattern. The rather simple proof uses Furstenberg's topological multiple recurrence theorem.

Publication Title

Discrete and Continuous Dynamical Systems - Series S

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