On the Number of Simple Arrangements of Five Double Pseudolines

Julien Ferté; Vincent Pilaud; Michel Pocchiola

doi:10.1007/s00454-010-9298-4

On the Number of Simple Arrangements of Five Double Pseudolines

Julien Ferté
, Vincent Pilaud
, Michel Pocchiola

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	279-302
Number of pages	24
Journal	Discrete and Computational Geometry
Volume	45
Issue number	2
DOIs	https://doi.org/10.1007/s00454-010-9298-4
Publication status	Published - 1 Mar 2011

Keywords

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

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10.1007/s00454-010-9298-4

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title = "On the Number of Simple Arrangements of Five Double Pseudolines",

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.",

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AU - Pilaud, Vincent

AU - Pocchiola, Michel

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N2 - 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.

AB - 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.

KW - Arrangements of double pseudolines

KW - Arrangements of pseudolines

KW - Chirotopes

KW - Combinatorial geometry

KW - Convexity

KW - Enumeration algorithms

KW - Mutations

KW - One-extension spaces

KW - Two-dimensional projective geometries

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DO - 10.1007/s00454-010-9298-4

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SP - 279

EP - 302

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 2

ER -

On the Number of Simple Arrangements of Five Double Pseudolines

Abstract

Keywords

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