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Ovale in STS(13). (English) Zbl 0551.05023

It is well-known that there are precisely two Steiner triple systems on 13 points. The paper under review establishes this fact synthetically via the use of ovals. [Ovals in projective and in more general 2-designs were introduced by the reviewer and J. H. van Lint, J. Comb. Theory, Ser. A 27, 307-324 (1979; Zbl 0422.05022).] The method used is undoubtedly more interesting than a purely computational approach. [The interested reader should compare this paper with N. N. Roghelia and S. S. Sane, Classification of (16,6,2)-designs by ovals, Discrete Math. 51, 167-177 (1984).]
Reviewer: E.F.Assmuss

MSC:

05B07 Triple systems
05B25 Combinatorial aspects of finite geometries

Keywords:

ovals; 2-designs

Citations:

Zbl 0422.05022
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