Abstract
Abstract : The incidence matrix A of a (v,k,lambda)-design satisfies A(A superscript T) + (k - lambda)I + lambda J, where (A superscript T) denotes the transpose of A. The matrix I is the identity matrix and the matrix J is the matrix of 1's. This equation occurs repeatedly in one form or another throughout the literature on combinatorial designs. In the present paper we alter the left side of the equation drastically and investigate XY = (k - lambda)I + lambda J, where X and Y are nonnegative integral matrices of sizes n by m and m by n, respectively. We take n > 1 and k not equal to lambda. The new equation is still open to a purely set theoretic interpretation. (Author)
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