The Spectrum of Orthogonal Steiner Triple Systems Academic Article uri icon

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abstract

  • AbstractTwo Steiner triple systems (V, ) and (V, ) are orthogonal if they have no triples in common, and if for every two distinct intersecting triples {x,y,z} and {x, y, z} of �, the two triples {x,y,a} and {u, v, b} in (� satisfy a ≠ b. It is shown here that if v ≡ 1,3 (mod 6), v ≥ 7 and v ≠ 9, a pair of orthogonal Steiner triple systems of order v exist. This settles completely the question of their existence posed by O'Shaughnessy in 1968.

authors

  • Colbourn, Charles J
  • Gibbons, Peter B
  • Mathon, Rudolf
  • Mullin, Ronald C
  • Rosa, Alexander

publication date

  • April 1, 1994