The Coven–Meyerowitz tiling conditions for 3 odd prime factors
The Coven–Meyerowitz tiling conditions for 3 odd prime factors
Abstract It is well known that if a finite set $$A\subset \mathbb {Z}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>⊂</mml:mo> <mml:mi>Z</mml:mi> </mml:mrow> </mml:math> tiles the integers by translations, then the translation set must be periodic, so that the tiling is equivalent to a factorization $$A\oplus B=\mathbb {Z}_M$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>⊕</mml:mo> …