Tiling the integers with translates of one tile: the Coven-Meyerowitz tiling conditions for three prime factors

Abstract: It is well known that if a finite set of integers A tiles the integers by translations, then the translation set must be periodic, so that the tiling is equivalent to a factorization A+B=Z_M of a finite cyclic group. Coven and Meyerowitz (1998) proved that when the tiling period M has at most two distinct prime factors, each of the sets A and B can be replaced by a highly ordered "standard" tiling complement. It is not known whether this behavior persists for all tilings with no restrictions on the number of prime factors of M.

In an ongoing collaboration with Izabella Laba, we proved that this is true when M=(pqr)^2. In my talk I will discuss this problem and introduce the main ingredients in the proof.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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