Tiling with arbitrary tiles

2015/05/14 by Gruslys, Vytautas, Leader, Imre, Tan, Ta Sheng
#05B45 #05B50 #52C22 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1505.03697

Abstract

Let T be a tile in ℤⁿ, meaning a finite subset of ℤⁿ. It may or may not tile ℤⁿ, in the sense of ℤⁿ having a partition into copies of T. However, we prove that T does tile ℤ^d for some d. This resolves a conjecture of Chalcraft.

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• A note on reduction of tiling problems
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