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Let be a family of random independent k-element subsets of [n] = 1,2,...,n and let denote a family of ℓ-element subsets of [n] such that the event that S belongs to depends only on the edges of contained in S. Then, the edges of are ’weakly dependent’, say, the events that two given subsets S and T are in are independent for vast majority of pairs S and T. In the paper we present some results on the structure of weakly dependent families of subsets obtained in this way. We also list...
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