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Complete Combinatorial Generation of Small Point Configurations and Hyperplane Arrangements
Lukas Finschi and Komei Fukuda
2001 April 30
Extended abstract presented in: Thirteenth Canadian Conference on Computational Geometry [CCCG 2001], University of Waterloo, 2001, pp. 97-100 (2001)
Abstract
A recent progress on the complete enumeration of oriented matroids enables us to generate all combinatorial types of small point configurations and hyperplane arrangements in general dimension, including degenerate ones. This extends a number of former works which concentrated on the nondegenerate case and are usually limited to dimension 2 or 3. Our initial study on the complete list for small cases has shown its potential in resolving geometric conjectures.
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