Author:
Colbourn Charles J.,Gibbons Peter B.,Mathon Rudolf,Mullin Ronald C.,Rosa Alexander
Abstract
AbstractTwo Steiner triple systems (V, 𝓑) and (V, 𝓓) 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 𝓑, the two triples {x,y,a} and {u, v, b} in (𝓓 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.
Publisher
Canadian Mathematical Society
Cited by
10 articles.
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