SYMMETRIC DESIGNS AND RELATED CONFIGURATIONS,

Combinatorial designs are considered which are characterized by a 0,1-matrix A of order n or 3 that satisfies the matrix equation A superscript TA D the square root of lambda sub ithe square root of lambda sub j, where A superscript T denotes the transpose of A, D denotes the diagonal matrix D diag k sub 1 - lambda sub 1, k sub 2- lambda sub 2, ..., k sub n- lambda sub n, and the scalars k sub i - lambda sub i and lambda sub j are positive. These configurations are called multiplicative designs. They are a natural generalization of the classical symmetric block designs and the recently investigated lambda-designs. Basic properties of multiplicative designs are developed. But the complete structure of these interesting configurations is far from determined. Author