Periodicity and decidability of translational tilings by rational
polygonal sets
Periodicity and decidability of translational tilings by rational
polygonal sets
The periodic tiling conjecture asserts that if a region $\Sigma\subset \mathbb R^d$ tiles $\mathbb R^d$ by translations then it admits at least one fully periodic tiling. This conjecture is known to hold in $\mathbb R$, and recently it was disproved in sufficiently high dimensions. In this paper, we study the …