An Application of Topological Multiple Recurrence to Tiling

Details An Application of Topological Multiple Recurrence to Tiling An Application of Topological Multiple Recurrence to Tiling

2008-09-08

arxiv.org/abs/0809.1421v1

Mathematics

Dynamical Systems

Scientific paper

We show that given any tiling of Euclidean space, any geometric patterns 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.

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