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arXiv · 1505.03697

Tiling with arbitrary tiles

Vytautas Gruslys·Imre Leader·Ta Sheng Tan
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Abstract

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

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Vytautas Gruslys, Imre Leader, Ta Sheng Tan. 2016-08-21. Tiling with arbitrary tiles. https://arxiv.org/abs/1505.03697

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