Details
| Original language | English |
|---|---|
| Pages (from-to) | 682-701 |
| Number of pages | 20 |
| Journal | Discrete and Computational Geometry |
| Volume | 48 |
| Issue number | 3 |
| Publication status | Published - 1 Oct 2012 |
| Externally published | Yes |
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.
Keywords
- Arrangement of hyperplanes, Pseudoline, Simplicial, Wiring
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Geometry and Topology
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Computer Science(all)
- Computational Theory and Mathematics
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In: Discrete and Computational Geometry, Vol. 48, No. 3, 01.10.2012, p. 682-701.
Research output: Contribution to journal › Article › Research › 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 -