Random paths through rectangles and cubes
β Scribed by Rodney Coleman
- Publisher
- Elsevier Science
- Year
- 1973
- Weight
- 407 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0026-0800
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π SIMILAR VOLUMES
We provide the discrete cube Q N = -1 1 N with its uniform probability, and we consider an independent sequence ΞΎ 1 ΞΎ N uniformly distributed on Q N . Kim and Roche recently proved that there exists Ξ΅ > 0 such that the probability that there exists (resp. does not exist) a point x of Q N with ΞΎ k β’
In this note we are concerned with the existence of matchings and families of disjoint paths between subsets of the n-dimensional discrete cube Qn. For example, we show that if A is a subset of Qn of size C:=,(;), where k c 4% then there is a matching from A to its complement of size at least (;).