Tiling the integers with translates of one finite set

Details Tiling the integers with translates of one finite set Tiling the integers with translates of one finite set

1998-02-27

arxiv.org/abs/math/9802122v1

Mathematics

Combinatorics

12 pages

Scientific paper

A set is said to tile the integers if and only if the integers can be written as a disjoint union of translates of that set. We consider the problem of finding necessary and sufficient conditions for a finite set to tile the integers. For sets of prime power size, it was solved by D. Newman [J. Number Theory 9 (1977), 107--111]. We solve it for sets of size having at most two prime factors. The conditions are always sufficient, but it is unknown whether they are necessary for all finite sets.

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