On the finite set of missing geometric configurations (n4)

Jürgen Bokowski*, Lars Schewe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We present various methods that have reduced the finite set of missing geometric configurations (n4). We show that there is no geometric configuration (174), and we provide examples for the former unknown cases n=18, n=29, n=31 - there do exist geometric configurations (n4). To construct these we use methods from computer algebra and optimization.

Original languageEnglish
Pages (from-to)532-540
Number of pages9
JournalComputational Geometry
Volume46
Issue number5
Early online date25 Nov 2011
DOIs
Publication statusPublished - 1 Jul 2013

Keywords

  • Geometric point line configuration
  • Oriented matroid
  • Projective incidence theorem
  • Pseudoline
  • Realization space

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