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Construction of Steiner Triple Systems Having Exactly One Triple in Common

Published online by Cambridge University Press:  20 November 2018

Charles C. Lindner
Charles C. Lindner*
Affiliation:
Auburn University, Auburn, Alabama
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A Steiner triple system is a pair (Q, t) where Q is a set and t a collection of three element subsets of Q such that each pair of elements of Q belong to exactly one triple of t. The number |Q| is called the order of the Steiner triple system (Q, t). It is well-known that there is a Steiner triple system of order n if and only if n ≡ 1 or 3 (mod 6). Therefore in saying that a certain property concerning Steiner triple systems is true for all n it is understood that n ≡ 1 or 3 (mod 6). Two Steiner triple systems (Q, t1) and (Q, t2) are said to be disjoint provided that t1 ∩ t2 = Ø. Recently, Jean Doyen has shown the existence of a pair of disjoint Steiner triple systems of order n for every n ≧ 7 [1].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 225 - 232
Copyright
Copyright © Canadian Mathematical Society 1974

References

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