Discrete & Computational Geometry

, Volume 4, Issue 4, pp 345–348

On representing sylvester-gallai designs

  • Endre Boros
  • Zoltan Füredi
  • L. M. Kelly
Article

Abstract

A misstated conjecture in [3] leads to an interesting “(1, 3) representation” of the 7-point projective plane inR4 where points are represented by lines and planes by 3-spaces. The corrected form of the original conjecture will be negated if there is a (1, 3) representation of the 13-point projective plane inR4 but that matter is not settled.

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References

  1. 1.
    Hirzebruch, F., Arrangements of Lines and Algebraic Surfaces, inArithmetic and Geometry (Papers dedicated to I. R. Shafarevich), Vol. 2, pp. 113–140, Birkhäuser, Basel, 1983.Google Scholar
  2. 2.
    Joussen, J., Eine Bemerkung zu einem Satz von Sylvester, inResults in Mathematics, Vol. 7, pp. 190–191, Birkhäuser, Basel, 1984.Google Scholar
  3. 3.
    Kelly, L. M., A Resolution of the Sylvester-Gallai Problem of J.-P. Serre,Discrete Comput. Geom. 1 (1986), 101–104.MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Kelly, L. M. and Nwankpa, S., Affine Embeddings of Sylvester-Gallai Designs,J. Combin. Theory 14 (1973), 422–438.MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Serre, J.-P., Problem 5359,Amer. Math. Monthly,73 (1966), 89.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Endre Boros
    • 1
  • Zoltan Füredi
    • 1
  • L. M. Kelly
    • 2
  1. 1.Mathematical InstituteHungarian Academy of ScienceBudapestHungary
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

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