Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 682-701 |
| Seitenumfang | 20 |
| Fachzeitschrift | Discrete and Computational Geometry |
| Jahrgang | 48 |
| Ausgabenummer | 3 |
| Publikationsstatus | Veröffentlicht - 1 Okt. 2012 |
| Extern publiziert | Ja |
Abstract
We compute all isomorphism classes of simplicial arrangements in the real projective plane with up to 27 lines. It turns out that Grünbaum's catalogue is complete up to 27 lines except for four new arrangements with 22, 23, 24, 25 lines, respectively. As a byproduct we classify simplicial arrangements of pseudolines with up to 27 lines. In particular, we disprove Grünbaum's conjecture about unstretchable arrangements with at most 16 lines, and prove the conjecture that any simplicial arrangement with at most 14 pseudolines is stretchable.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Theoretische Informatik
- Mathematik (insg.)
- Geometrie und Topologie
- Mathematik (insg.)
- Diskrete Mathematik und Kombinatorik
- Informatik (insg.)
- Theoretische Informatik und Mathematik
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in: Discrete and Computational Geometry, Jahrgang 48, Nr. 3, 01.10.2012, S. 682-701.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Simplicial Arrangements with up to 27 Lines
AU - Cuntz, M.
PY - 2012/10/1
Y1 - 2012/10/1
N2 - We compute all isomorphism classes of simplicial arrangements in the real projective plane with up to 27 lines. It turns out that Grünbaum's catalogue is complete up to 27 lines except for four new arrangements with 22, 23, 24, 25 lines, respectively. As a byproduct we classify simplicial arrangements of pseudolines with up to 27 lines. In particular, we disprove Grünbaum's conjecture about unstretchable arrangements with at most 16 lines, and prove the conjecture that any simplicial arrangement with at most 14 pseudolines is stretchable.
AB - We compute all isomorphism classes of simplicial arrangements in the real projective plane with up to 27 lines. It turns out that Grünbaum's catalogue is complete up to 27 lines except for four new arrangements with 22, 23, 24, 25 lines, respectively. As a byproduct we classify simplicial arrangements of pseudolines with up to 27 lines. In particular, we disprove Grünbaum's conjecture about unstretchable arrangements with at most 16 lines, and prove the conjecture that any simplicial arrangement with at most 14 pseudolines is stretchable.
KW - Arrangement of hyperplanes
KW - Pseudoline
KW - Simplicial
KW - Wiring
UR - http://www.scopus.com/inward/record.url?scp=84865637465&partnerID=8YFLogxK
U2 - 10.1007/s00454-012-9423-7
DO - 10.1007/s00454-012-9423-7
M3 - Article
AN - SCOPUS:84865637465
VL - 48
SP - 682
EP - 701
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
SN - 0179-5376
IS - 3
ER -