The Intersection Problem for Steiner Triple Systems

Abstract

In this thesis we give a new solution to the intersection problem for Steiner triple systems, using results that were not available when the original solution was given. In particular we show for each pair (n,k), where n is congruent to 1 or 3 (mod 6), for n greater than or equal to 19, and k is an element of {0,1,2,...,x=(n(n-1))/6}\{x-1,x-2,x-3,x-5}, the existence of a pair of Steiner triple systems of order n with k triples in common.