Simplicial arrangements with up to 27 lines
M Cuntz - Discrete & computational geometry, 2012 - Springer
Discrete & computational geometry, 2012•Springer
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.
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.
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.
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