Details
| Original language | English |
|---|---|
| Pages (from-to) | 107-124 |
| Number of pages | 18 |
| Journal | Discrete & computational geometry |
| Volume | 68 |
| Issue number | 1 |
| Early online date | 20 Dec 2021 |
| Publication status | Published - Jul 2022 |
Abstract
Keywords
- math.CO, 20F55, 52C35, 14N20, Reflection group, Matroid, Simplicial arrangement
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Geometry and Topology
- Computer Science(all)
- Computational Theory and Mathematics
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In: Discrete & computational geometry, Vol. 68, No. 1, 07.2022, p. 107-124.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A Greedy Algorithm to Compute Arrangements of Lines in the Projective Plane
AU - Cuntz, Michael
N1 - Funding Information: The computations required for the results of this paper were performed on a computer cluster funded by the DFG, project number 411116428.
PY - 2022/7
Y1 - 2022/7
N2 - 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.
AB - 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.
KW - math.CO
KW - 20F55, 52C35, 14N20
KW - Reflection group
KW - Matroid
KW - Simplicial arrangement
UR - http://www.scopus.com/inward/record.url?scp=85121430085&partnerID=8YFLogxK
U2 - 10.1007/s00454-021-00351-y
DO - 10.1007/s00454-021-00351-y
M3 - Article
VL - 68
SP - 107
EP - 124
JO - Discrete & computational geometry
JF - Discrete & computational geometry
SN - 0179-5376
IS - 1
ER -