
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 lambdadesigns. 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