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

verfasst von
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.

Organisationseinheit(en)
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Typ
Preprint
Anzahl der Seiten
15
Publikationsdatum
25.06.2020
Publikationsstatus
Elektronisch veröffentlicht (E-Pub)
Elektronische Version(en)
https://arxiv.org/abs/2006.14431 (Zugang: Offen)