Abstract
The classical Erdýos-Ko-Rado (EKR) Theorem states that if we choose a family of subsets, each of size k, from a fixed set of size n (n > 2k), then the largest possible pairwise intersecting family has size t = n 1 k 1 � . We consider the probability that a randomly selected family of size t = tn has the EKR property (pairwise nonempty intersection) as n and k = kn tend to infinity, the latter at a specific rate. As t gets large, the EKR property is less likely to occur, while as t gets smaller, the EKR property is satisfied with high probability. We derive the threshold value for t using Janson’s inequality. Using the Stein-Chen method we show that the distribution of X0, defined
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