Abstract
Cube tilings formed by n-dimensional 4ℤn-periodic hypercubes with side 2 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.
Original language | English |
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Pages (from-to) | 1112-1122 |
Number of pages | 11 |
Journal | Discrete and Computational Geometry |
Volume | 50 |
Issue number | 4 |
DOIs | |
Publication status | Published - Dec 2013 |
Keywords
- Classification
- Cube tilings
- Exact cover
- Switching graph
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics