On the Intersection Problem for Steiner Triple Systems of Different Orders.

A Steiner triple system of order v, or STS( v), is a pair ( V, [InlineMediaObject not available: see fulltext.]) with V a set of v points and [InlineMediaObject not available: see fulltext.] a set of 3-subsets of V called blocks or triples, such that every pair of distinct elements of V occurs in exactly one triple. The intersection problem for STS is to determine the possible numbers of blocks common to two Steiner triple systems STS( u), ( U, [InlineMediaObject not available: see fulltext.]), and STS( v), ( V, [InlineMediaObject not available: see fulltext.]), with U⊆ V. The case where U= V was solved by Lindner and Rosa in 1975. Here, we let U⊂ V and completely solve this question for v− u=2,4 and for v≥2 u−3. [ABSTRACT FROM AUTHOR]