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29 March 2024
 
  » arxiv » 0807.2500

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The fine intersection problem for Steiner triple systems
Yeow Meng Chee ; Alan C. H. Ling ; Hao Shen ;
Date 16 Jul 2008
AbstractThe 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).
Source arXiv, 0807.2500
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