A Note on P.B.I.B. Design Matrices

Abstract

The notation P.B.I.B. $(m)$ will mean partially balanced incomplete block design with $m$ associative classes. It is found that the $C$ matrix of a P.B.I.B $(m)$ may be expressed as a linear function of $m + 1$ commutative and linearly independent matrices. The author feels that this decomposition may be of interest to those studying the properties of P.B.I.B. designs.