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
Recommended Citation
De La Llave, R., & Windsor, A. (2009). An application of topological multiple recurrence to tiling. Discrete and Continuous Dynamical Systems - Series S, 2 (2), 315-324. https://doi.org/10.3934/dcdss.2009.2.315
COinS
