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The Spectrum of Orthogonal Steiner Triple Systems

Published online by Cambridge University Press:  20 November 2018

Charles J. Colbourn ,
Peter B. Gibbons ,
Rudolf Mathon ,
Ronald C. Mullin  and
Alexander Rosa
Charles J. Colbourn
Affiliation:
Combinatorics and Optimization University of Waterloo Waterloo, Ontario N2L 3G1
Peter B. Gibbons
Affiliation:
Computer Science University of Auckland Auckland New Zealand
Rudolf Mathon
Affiliation:
Computer Science University of Toronto Toronto, Ontario M5S I A4
Ronald C. Mullin
Affiliation:
Combinatorics and Optimization University of Waterloo Waterloo, Ontario N2L 3G1
Alexander Rosa
Affiliation:
Mathematics and Statistics McMaster University Hamilton, Ontario L8S4K1
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Abstract

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Two 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.

Keywords

05B07
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 2 , 01 April 1994 , pp. 239 - 252
Copyright
Copyright © Canadian Mathematical Society 1994

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