Tiling the integers with translates of one finite set

dc.creatorCoven, Ethan M.
dc.creatorMeyerowitz, Aaron D.
dc.date1998-02-27
dc.date.accessioned2026-07-07T05:23:57Z
dc.date.available2026-07-07T05:23:57Z
dc.descriptionA 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.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/9802122
dc.identifierhttp://arxiv.org/abs/math/9802122
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76647
dc.subjectCombinatorics
dc.subjectGroup Theory
dc.subject05B45 (Primary) 11B75, 20K01 (Secondary)
dc.titleTiling the integers with translates of one finite set
dc.typetext

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