A characterization of finite sets that tile the integers

2001/09/19 by Andrew Granville, Granville, Andrew, Izabella Laba +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.math/0109127

17 pages

arxiv created 2001/09/19 · arxiv updated 2009/11/30

Abstract

We consider the problem of characterizing finite sets which tile the integers by translations. Coven and Meyerowitz (J. Algebra 1999) found necessary and sufficient conditions for a finite set A to tile the integers under the assumption that |A| has at most 2 distinct prime factors. The purpose of this article is to settle, for the first time, certain three-prime cases.

Related

• Tiling the integers with translates of one finite set
• The Coven-Meyerowitz tiling conditions for 3 odd prime factors
• The Coven-Meyerowitz tiling conditions for 3 prime factors: the even case
• Functional tilings and the Coven-Meyerowitz tiling conditions
• Splitting for integer tilings