, Volume 20, Issue 2, pp 155-161

Straight line arrangements in the real projective plane

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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.

This work was done while the second author was doing a Postdoc visiting the Université Pierre et Marie Curie, Paris 6, Equipe Combinatoire and was partially supported by a fellowship from the European Commission, Contract No. ERBCI1*CT940606. His current address is Université Pierre et Marie Curie, Paris 6, case 189 — Combinatoire, 4 place Jussieu, 75252 Paris Cedex 05, France.