Translational Tilings of the Integers with Long Periods
Translational Tilings of the Integers with Long Periods
Suppose that $A \subseteq {\Bbb{Z}}$ is a finite set of integers of diameter $D=\max A - \min A$. Suppose also that $B \subseteq {\Bbb{Z}}$ is such that $A\oplus B = {\Bbb{Z}}$, that is each $n\in{\Bbb{Z}}$ is uniquely expressible as $a+b$, $a\in A$, $b\in B$. We say then that $A$ tiles …