On the finite set of missing geometric configurations (n4)

Authors:
JüRgen Bokowski;Lars Schewe
Affiliations:
Technical University Darmstadt, Schloígartenstraíe 7, 64287, Darmstadt, Germany;Technical University Darmstadt, Schloígartenstraíe 7, 64287, Darmstadt, Germany
Venue:
Computational Geometry: Theory and Applications
Year:
2013

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Abstract

We present various methods that have reduced the finite set of missing geometric configurations (n"4). We show that there is no geometric configuration (17"4), and we provide examples for the former unknown cases n=18, n=29, n=31 - there do exist geometric configurations (n"4). To construct these we use methods from computer algebra and optimization.