Latin cubes of order ⩽5
✍ Scribed by Gary L. Mullen; Robert E. Weber
- Book ID
- 103057029
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 237 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
A general method to construct third-order magic cubes and hypercubes is described. It is shown that magic hypercubes of order 3 must be symmetrical and there are exactly 58 such hypercubes in 4-dimensional space, not counting rotations and reflections.
A (maximal) difference matrix with r rows over a group G of order s gives rise to a (maximal) set of r -1 mutually orthogonal Latin squares of order s. The row sizes of maximal difference matrices are determined for all groups G of order ~<10.
## Abstract Necessary conditions for the complete graph on __n__ vertices to have a decomposition into 5‐cubes are that 5 divides __n__ − 1 and 80 divides __n__(__n__ − 1)/2. These are known to be sufficient when __n__ is odd. We prove them also sufficient for __n__ even, thus completing the spectr