Abstract
We prove that if ( S 1, β 1) and ( S 2, β 2) are two Steiner triple systems of order v and if S is a set of v points, then there exist two disjoint Steiner triple systems ( S, β 1′) and ( S, β 2′) with ( S 1, β 1) ≅ ( S, β 1′) and ( S 2, β 2) ≅ ( S, β 2′).
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