On-line covering the unit cube by cubes
β Scribed by J. Januszewski; M. Lassak
- Book ID
- 110561256
- Publisher
- Springer
- Year
- 1994
- Tongue
- English
- Weight
- 256 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0179-5376
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
One can easily cover the vertices of the \(n\)-cube by 2 hyperplanes. Here it is proved that any set of hyperplanes that covers all the vertices of the \(n\)-cube but one contains at least \(n\) hyperplanes. We give a variety of proofs and generalizations.
Let Q n be the (hyper)cube [&1, 1] n . This paper is concerned with the following question: How many vectors must be chosen uniformly and independently at random from Q n before every vector in Q n itself has negative inner product with at least one of the random vectors? For any fixed =>0, a simple