In this paper we are concerned with the following conjecture. Conjecture: Let L be a collection of k positive integers and A = {A_t,..., A_m} denote a family of subsets of an n-element set such that the point |A_i intersect A_j| belong to (is member of) the set L, for all A_i, A_j implied by A, then |A| <= #SIGMA#_(i = 0)~k (_i~(n - 1)). In particular, we show this conjecture is true when L consists of k consecutive positive integers. This generalizes a well-known inequality of Fisher's. Our proof simplifies and extends a recent result of Ramanan's.
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