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Characterization of complete exterior sets of conics

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Abstract

Let ε be a set of\(\frac{{q + 1}}{2}\) exterior points of a nondegenerate conic inPG(2,q) with the property that the line joining any 2 points in ε misses the conic. Ifq≡1 (mod 4) then ε consists of the exterior points on a passant, ifq≡3 (mod 4) then other examples exist (at least forq=7, 11, ..., 31).

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References

  1. A. Blokhuis, Á. Seress, andH.A. Wilbrink: On sets of points without tangents.Mitt. Math. Sem. Giessen 201 (1991), 39–44.

    MathSciNet  MATH  Google Scholar 

  2. A. A. Bruen: Inversive Geometry and some New Planes,Geom. Dedicata 7 (1978), 81–98.

    MathSciNet  MATH  Google Scholar 

  3. A. A. Bruen, andB. Levinger: A theorem on permutations of a finite field,Canadian Journal of Mathematics 25 (1973), 1060–1065.

    Article  MathSciNet  Google Scholar 

  4. L. Carlitz: A theorem on permutations in a finite field,Proc. American Mathematical Society 11 (1960), 456–459.

    Article  MathSciNet  Google Scholar 

  5. G. Korchmáros: Example of a chain of circles on an Elliptic Quadric ofPG(3, q), q=7,11Journal of Comb. Theory, A31 (1981), 98–100.

    Article  Google Scholar 

  6. R. McConnel: Pseudo-ordered polynomials over a finite field,Acta Arithmetica 8 (1963), 127–151.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, Den Dolech 2, The Netherlands

    A. Blokhuis & H. A. Wilbrink

  2. Mathematical Institute of the Hungarian Academy of Sciences, H-1053, Budapest, Hungary

    Á Seress

  3. The Ohio State University, 43210, Columbus, OH, USA

    Á Seress

Authors
  1. A. Blokhuis
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  2. Á Seress
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  3. H. A. Wilbrink
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Additional information

Support from the Dutch organization for scientific Research (NWO) is gratefully acknowledged

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Blokhuis, A., Seress, Á. & Wilbrink, H.A. Characterization of complete exterior sets of conics. Combinatorica 12, 143–147 (1992). https://doi.org/10.1007/BF01204717

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  • DOI: https://doi.org/10.1007/BF01204717

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