Discrete & Computational Geometry

, Volume 45, Issue 2, pp 279–302 | Cite as

On the Number of Simple Arrangements of Five Double Pseudolines

Article

Abstract

We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the connectedness under mutations of the spaces of one-extensions of double pseudoline arrangements, proved in this paper. Counting results derived from an implementation of our algorithm are also reported.

Keywords

Combinatorial geometry Convexity Two-dimensional projective geometries Arrangements of pseudolines Arrangements of double pseudolines Chirotopes Mutations One-extension spaces Enumeration algorithms 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Julien Ferté
    • 1
  • Vincent Pilaud
    • 2
  • Michel Pocchiola
    • 2
  1. 1.Laboratoire d’Informatique FondamentaleUniversité de ProvenceMarseilleFrance
  2. 2.Équipe Combinatoire et OptimisationUniversité Pierre et Marie CurieParisFrance

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