Discrete & Computational Geometry

, Volume 4, Issue 4, pp 345–348 | Cite as

On representing sylvester-gallai designs

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


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.


Projective Plane Discrete Comput Geom Liberal Representation Finite Family Serre Result 
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  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
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    Joussen, J., Eine Bemerkung zu einem Satz von Sylvester, inResults in Mathematics, Vol. 7, pp. 190–191, Birkhäuser, Basel, 1984.Google Scholar
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    Kelly, L. M., A Resolution of the Sylvester-Gallai Problem of J.-P. Serre,Discrete Comput. Geom. 1 (1986), 101–104.MATHMathSciNetCrossRefGoogle Scholar
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    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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