Accession Number : AD0694537

Title :   SYMMETRIC DESIGNS AND RELATED CONFIGURATIONS,

Corporate Author : CALIFORNIA INST OF TECH PASADENA

Personal Author(s) : Ryser,H. J.

Report Date : AUG 1969

Pagination or Media Count : 22

Abstract : 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 T)A = D + ((the square root of (lambda sub i))(the 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)

Descriptors :   (*MATRICES(MATHEMATICS), *COMBINATORIAL ANALYSIS), PERMUTATIONS, INEQUALITIES, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE