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Abstract Upper and lower bounds are given for P ( S ≤ k ), 0 ≤ k ≤ ES , where S is a sum of indicator variables with a special structure, which appears, for example, in subgraph counts in random graphs. in typical cases, these bounds are close to the corresponding probabilities for a Poisson distribution with the same mean as S . There are no corresponding general bounds for P ( S ≥ k ), k > ES , but some partial results are given.
Svante Janson (Fri,) studied this question.