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Discrete & Computational Geometry

, Volume 20, Issue 2, pp 155–161 | Cite as

Straight line arrangements in the real projective plane

  • D. Forge
  • J. L. Ramírez Alfonsín
Article

Abstract

Let A be an arrangement of n pseudolines in the real projective plane and let p 3(A) be the number of triangles of A. Grünbaum has proposed the following question. Are there infinitely many simple arrangements of straight lines with p 3(A)=1/3n(n−1)? In this paper we answer this question affirmatively.

Keywords

Discrete Comput Geom Marie Curie Infinite Family Recursive Method Line Arrangement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    B. Grünbaum, Arrangements and Spreads, Regional Conference Series in Mathematics, Vol. 10, American Mathematical Society, Providence, RI, 1972.Google Scholar
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    H. Harborth, Two-colorings of simple arrangements, in Finite and Infinite Sets, Colloquia Mathematica Societatis János Bolyai, Vol. 37, North-Holland, Amsterdam, 1981, pp. 371–378.Google Scholar
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    J.-R Roudneff, On the number of triangles in simple arragements of pseudolines in the real projective plane, Discrete Mathematics 60 (1986), 243–251.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • D. Forge
    • 1
  • J. L. Ramírez Alfonsín
    • 2
  1. 1.Université Pierre et Marie Curie, Paris 6, case 189Paris Cedex 05France
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de México, Area de la Investigacion Cientifica, Circuito Exterior, C.U.Mexico

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