Tiling the integers with translates of one finite set
| dc.creator | Coven, Ethan M. | |
| dc.creator | Meyerowitz, Aaron D. | |
| dc.date | 1998-02-27 | |
| dc.date.accessioned | 2026-07-07T05:23:57Z | |
| dc.date.available | 2026-07-07T05:23:57Z | |
| dc.description | 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. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/9802122 | |
| dc.identifier | http://arxiv.org/abs/math/9802122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76647 | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 05B45 (Primary) 11B75, 20K01 (Secondary) | |
| dc.title | Tiling the integers with translates of one finite set | |
| dc.type | text |