Accession Number : AD0684099

Title :   COMBINATORIAL DESIGNS AND RELATED SYSTEMS,

Corporate Author : CALIFORNIA INST OF TECH PASADENA

Personal Author(s) : Bridges,W. G. ; Ryser,H. J.

Report Date : 1969

Pagination or Media Count : 26

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)

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

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE