Name
Abstract | ||
|---|---|---|
Cube tilings formed by -dimensional -periodic hypercubes with side and integer coordinates are considered here. By representing the problem of finding such cube tilings within the framework of exact cover and using canonical augmentation, pairwise nonisomorphic 5-dimensional cube tilings are exhaustively enumerated in a constructive manner. There are 899,710,227 isomorphism classes of such tilings, and the total number of tilings is 638,560,878,292,512. It is further shown that starting from a 5-dimensional cube tiling and using a sequence of switching operations, it is possible to generate any other cube tiling. |
Year | DOI | Venue |
|---|---|---|
2013 | https://doi.org/10.1007/s00454-013-9547-4 | Discrete & Computational Geometry |
Keywords | Field | DocType |
Cube tilings,Classification,Exact cover,Switching graph | Integer,Discrete mathematics,Topology,Combinatorics,Substitution tiling,Exact cover,Isomorphism,Triangular tiling,Tessellation,Mathematics,Hypercube,Cube | Journal |
Volume | Issue | ISSN |
50 | 4 | 0179-5376 |
Citations | PageRank | References |
1 | 0.38 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| K. Ashik Mathew | 1 | 12 | 1.75 |
| Patric R. J. Östergård | 2 | 609 | 70.61 |
| Alexandru Popa | 3 | 70 | 13.34 |