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Detine A(n) to be the largest integer such that for each set A of size n and cover 9 of A, there exist EC_ A and Q c F such that IBI = L(n) and the restriction of Q to B is a partition of B. It is shown that when n 2 3 n-<i.(n)< 2(n-1) (1 +Inn) (I +Ig(n-l)-lglg(n-1)) The lower bound is proved by a probabilistic method. A related probabilistic algorithm for… (More)

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