Probabilities for intersecting systems and random subsets of finite sets
SIAM Journal on Algebraic and Discrete Methods
The complete intersection theorem for systems of finite sets
European Journal of Combinatorics
The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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Let p ≤ 1/2 and let µp be the product measure on {0, 1}n, where µp(x) = pΣxi(1 - p)n-Σxi. Let A ⊂ {0, 1}n be an intersecting family, i.e. for every x, y ∈ A there exists 1 ≤ i ≤ n such that xi = Yi = 1. Then µp(A) ≤ p. Our proof uses a probabilistic trick first applied by Katona to prove the Erdös-Ko-Rado theorem.