The fine intersection problem for Steiner triple systems

Yeow Meng Chee, Alan C. H. Ling, Hao Shen

Published 2008-07-16Version 1

The intersection of two Steiner triple systems (X,A) and (X,B) is the set A intersect B. The fine intersection problem for Steiner triple systems is to determine for each v, the set I(v), consisting of all possible pairs (m,n) such that there exist two Steiner triple systems of order v whose intersection has n blocks over m points. We show that for v = 1 or 3 (mod 6), |I(v)| = Omega(v^3), where previous results only imply that |I(v)| = Omega(v^2).