3 research outputs found
A Greedy Algorithm to Compute Arrangements of Lines in the Projective Plane
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. © 2021, The Author(s)
A greedy algorithm to compute arrangements of lines in the projective plane
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.Comment: 15 pages, 2 figure