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Small complete arcs in andré planes of square order

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Abstract

A complete arc in a projective plane of orderq has at least\(\sqrt {2q} \) points. We show the existence of completek-arcs having\(k< C\sqrt q \log ^2 q\) points in certain André planes of square order. Moreover our construction shows that for all\(x,q > x > \sqrt q \log q\) there are completek-arcs withx < k < Cxlogq, for some absolute constantC.

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References

  1. Fisher, J.C.: Randomk-arcs. Preliminary report, 1989

  2. Füredi, Z.: Matchings and Covers in Hypergraphs, Graphs Comb.4, 115–206 (1988)

    Google Scholar 

  3. Hirschfeld, J.W.P.: Projective geometries over finite fields. Oxford: Clarendon Press 1976

    Google Scholar 

  4. Hughes, D.R., Piper, F.: Projective planes, Berlin: Springer-Verlag 1973

    Google Scholar 

  5. Lovász, L.: On the ratio of optimal integral and fractional covers. Discrete Math.13, 383–390 (1975)

    Google Scholar 

  6. Segre, B.: Introduction to Galois Geometries. Atti Accad. Naz. Lincei8, 135–236 (1967)

    Google Scholar 

  7. Segre, B.: Lectures on modern geometry. Roma: Cremonese 1961

    Google Scholar 

  8. Szönyi, T.: Complete arcs in Galois planes: a survey. Quad. Sem. Geom. Comb. Univ. Roma “La Sapienza”,94, (1989)

  9. Szönyi, T.: Complete arcs in non-desarguesian planes. Conf. Semin. Mat. Univ. Bari233 (1990)

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  1. Department of Computer Science, Eötvös Loránd University, Budapest, Múzeum krt. 6-8, H-1088, Budapest, Hungary

    Tamás Szönyi

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  1. Tamás Szönyi
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Szönyi, T. Small complete arcs in andré planes of square order. Graphs and Combinatorics 7, 279–287 (1991). https://doi.org/10.1007/BF01787635

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  • DOI: https://doi.org/10.1007/BF01787635

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