On the finite set of missing geometric configurations (n4)

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 us...

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Veröffentlicht in:	Computational geometry : theory and applications 2013-07, Vol.46 (5), p.532-540
Hauptverfasser:	Bokowski, Jürgen, Schewe, Lars
Format:	Artikel
Sprache:	eng
Schlagworte:	Computational geometry Computer algebra Construction Geometric point line configuration Mathematical analysis Optimization Oriented matroid Projective incidence theorem Pseudoline Realization space
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Zusammenfassung:	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.
ISSN:	0925-7721
DOI:	10.1016/j.comgeo.2011.11.001