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The flower intersection problem for Steiner triple systems. (English) Zbl 0675.05009

Combinatorial design theory, Dedic. A. Rosa Occas. 50th Birthday, Ann. Discrete Math. 34, 243-248 (1987).
Summary: [For the entire collection see Zbl 0625.00011.]
We determine here those pairs (k,v) for which there exist a pair of Steiner triple systems on the same v-set, the triples in one system containing a particular point are the same as those in the other system containing that point, and the two systems otherwise have exactly k triples in common. The obvious necessary conditions are sufficient, with two exceptions \((k,v)=(1,9)\) and (4,9).

MSC:

05B07 Triple systems
51E10 Steiner systems in finite geometry

Citations:

Zbl 0625.00011