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A greedy algorithm to compute arrangements of lines in the projective plane

authored by
Michael Cuntz
Abstract

We introduce a greedy algorithm optimizing arrangements of lines with respect to a property. We apply this algorithm to the case of simpliciality: it recovers all known simplicial arrangements of lines in a very short time and also produces a yet unknown simplicial arrangement with 35 lines. We compute a (certainly incomplete) database of combinatorially simplicial complex arrangements of hyperplanes with up to 50 lines. Surprisingly, it contains several examples whose matroids have an infinite space of realizations up to projectivities.

Organisation(s)
Institute of Algebra, Number Theory and Discrete Mathematics
Type
Preprint
No. of pages
15
Publication date
25.06.2020
Publication status
E-pub ahead of print
Electronic version(s)
https://arxiv.org/abs/2006.14431 (Access: Open)