# Accession Number:

## AD0684099

# Title:

## COMBINATORIAL DESIGNS AND RELATED SYSTEMS,

# Descriptive Note:

# Corporate Author:

## CALIFORNIA INST OF TECH PASADENA

# Personal Author(s):

# Report Date:

## 1969-01-01

# Pagination or Media Count:

## 26.0

# Abstract:

The incidence matrix A of a v,k,lambda-design satisfies AA superscript T k - lambdaI 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 1s. 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 - lambdaI 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

# Subject Categories:

- Theoretical Mathematics