Constructive Upper Bounds for Intersecting Set Systems
β Scribed by Vince Grolmusz
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 245 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1571-0653
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π SIMILAR VOLUMES
A family of r sets is called a 2-system if any two sets have the same intersection. Denote by F(n, r) the most number of subsets of an n-element set which do not contain a 2-system consisting of r sets. Constructive new lower bounds for F(n, r) are given which improve known probabilistic results, an
Erdos and Rado defined a A-system, as a family in which every two members have the same intersection. Here we obtain a new upper bound on the maximum cardinality q ( n , q ) of an n-uniform family not containing any A-system of cardinality q. Namely, we prove that, for any a > 1 and q , there exists