The fine intersection problem for Steiner triple systems

Details The fine intersection problem for Steiner triple systems The fine intersection problem for Steiner triple systems

2008-07-16

arxiv.org/abs/0807.2500v1

Mathematics

Combinatorics

9 pages

Scientific paper

10.1007/s00373-006-0690-z

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).

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