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 ลฝ . size, it was solved by D. Newman 1977, J. Numbe
Tiling the line with translates of one tile
โ Scribed by Jeffrey C. Lagarias; Yang Wang
- Book ID
- 105912388
- Publisher
- Springer-Verlag
- Year
- 1996
- Tongue
- English
- Weight
- 243 KB
- Volume
- 124
- Category
- Article
- ISSN
- 0020-9910
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๐ SIMILAR VOLUMES
General methods for finding tile-k-transitive filings of the three-dimensional Euclidean space with polyhedral bodies are discussed. Analogous methods for enumerating k-isohedral filings of a two-dimensional plane of constant curvature have been obtained previously.
In this paper , we consider a broad class of simply connected complexes that includes , for example , the face-to-face tilings of E n and S n . Along with a complex (or tiling) we consider a set แซ of qualities that individually can be assigned to the various cells or tiles of the complex , and a gro