Disjoint Intersection Problem For Steiner Triple Systems

Abstract

Let (S, T_1) and (S, T_2) be two Steiner Triple systems on the set S of symbols with the set of triples T_1 and T_2 respectively. They are said to intersect in m blocks if |T_1 intersection T_2| = m. Further, if the blocks in T_1 intersection T_2 are pairwise disjoint then (S, T_1) and (S, T_2) are said to intersect in m pairwise disjoint blocks and are said to have disjoint intersection.

The Disjoint Intersection Problem for Steiner Triple Systems is to completely determine Int_d(v) = set of all m such that, there exist two Steiner triple systems of order v intersecting in m pairwise disjoint blocks. Int_d(v) was determined by Chee. Here we describe a different proof of his result using a modification of the Bose and Skolem Constructions.