Tiling the Integers with Translates of One Finite Set
| Autor: | Aaron Meyerowitz, Ethan M. Coven |
|---|---|
| Rok vydání: | 1999 |
| Předmět: |
Discrete mathematics
Disjoint union Algebra and Number Theory 010102 general mathematics 0102 computer and information sciences Disjoint sets 01 natural sciences Set (abstract data type) Combinatorics symbols.namesake Closure (mathematics) 010201 computation theory & mathematics Eisenstein integer Prime factor symbols 0101 mathematics Finite set Prime power Mathematics |
| Zdroj: | Journal of Algebra. 212(1):161-174 |
| ISSN: | 0021-8693 |
| DOI: | 10.1006/jabr.1998.7628 |
| Popis: | A settiles the integersif 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 (1977,J. Number Theory9, 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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