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Tiling the Integers with Translates of One Finite Set

✍ Scribed by Ethan M. Coven; Aaron Meyerowitz

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
115 KB
Volume
212
Category
Article
ISSN
0021-8693

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✦ Synopsis

A set tiles 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 Ž . size, it was solved by D. Newman 1977, J. Number Theory 9, 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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