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Arcs and ovals in steiner triple systems

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Combinatorial Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 969))

Abstract

Several constructions of Steiner triple systems (STS) with ovals are given. For every v ≡ 3 or 7 mod 12 there are STS's with hyperovals, for every v ≡ 1 or 3 mod 6 there are STS's with ovals, and for infinitely many v ≡ 1 or 3 mod 6 there are STS's without ovals. The ovals may be classified by their complementary sets, the so-called counterovals. Several questions remain open.

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Author information

Authors and Affiliations

  1. Freie Universität, Königin-Luise-Str. 24-26, D-1000, Berlin 33

    Hanfried Lenz

  2. Universität Bayreuth, Universitätsstr. 30, D-8580, Bayreuth, Germany

    Herbert Zeitler

Authors
  1. Hanfried Lenz
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  2. Herbert Zeitler
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Editor information

Dieter Jungnickel Klaus Vedder

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© 1982 Springer-Verlag

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Lenz, H., Zeitler, H. (1982). Arcs and ovals in steiner triple systems. In: Jungnickel, D., Vedder, K. (eds) Combinatorial Theory. Lecture Notes in Mathematics, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062997

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  • DOI: https://doi.org/10.1007/BFb0062997

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11971-5

  • Online ISBN: 978-3-540-39380-1

  • eBook Packages: Springer Book Archive

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