Journal of the Australian Mathematical Society (Series A)

Table of Contents - 1977 - Volume 23, Issue 04  

Research Article

Some results on a combinatorial problem of Cordes

D. McCarthya1 and G. H. J. van Reesa1

a1 University of Waterloo, Waterloo, Ontario, Canada

Abstract

Cordes (1976) introduced the problem of determining the maximum number of resolution classes of a finite set partitioned into equicardinal subsets such that the number of pairs common to any 2 classes is minimized. A later paper of Mullin and Stanton (1976) investigated those conditions under which the configurations were actually BIBD's. They obtained a bound for these special configurations and conjectured it applied in general. We prove this in the present paper. A recursive and a direct construction are also given for a special class of configurations.

(Received July 19 1976)