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

Artikel

Journal

Discrete & computational geometry

Band

68

Seiten

107-124

Anzahl der Seiten

18

ISSN

0179-5376

Publikationsdatum

07.2022

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Theoretische Informatik, Diskrete Mathematik und Kombinatorik, Geometrie und Topologie, Theoretische Informatik und Mathematik

Elektronische Version(en)

https://arxiv.org/abs/2006.14431 (Zugang: Offen)
https://doi.org/10.1007/s00454-021-00351-y (Zugang: Offen)