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

Article

Journal

Discrete & computational geometry

Volume

68

Pages

107-124

No. of pages

18

ISSN

0179-5376

Publication date

07.2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Theoretical Computer Science, Discrete Mathematics and Combinatorics, Geometry and Topology, Computational Theory and Mathematics

Electronic version(s)

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