Design Theory, 2nd Edition

5

Kirkman Triple Systems

 

5.1 A recursive construction

In this chapter we will consider Steiner triple systems with the additional property of being resolvable. Not only will we consider when such systems exist, but also many different PBDs will be found, and in the process several important constructions for PBDs will be introduced. In fact, understanding the various constructions in Section 5.2 is more to the point than finding the PBDs themselves.

We begin with some definitions. A parallel class in a Steiner triple system ( S , T ) is a set of triples in T that partitions S. An STS ( S , T ) is resolvable if the triples in T can be partitioned into parallel classes. A resolvable STS(v) is also known as a Kirkman triple system ...