Design Theory, 2nd Edition

2

λ-Fold Triple Systems

 

2.1 Triple systems of index λ > 1

A λ -fold triple system (or a triple system of index λ .) is a pair ( S , T ) , where S is a finite set and T is a collection of 3-element subsets of S called triples such that each pair of distinct elements of S belongs to exactly λ triples of T. So, a Steiner triple system is a 1-fold triple system (or a triple system of index λ = 1 ). As with Steiner triple systems, the order of a λ -fold triple system ( S , T ) is the number | S | . Just as with Steiner triple systems we can think of a λ -fold triple system as a decomposition of λ K v , the graph with v vertices in which each vertex is joined by λ edges, into edge disjoint triangles.

It is ...