Simplicial arrangements with up to 27 lines
Combinatorics
2011-08-16 v1
Abstract
We compute all isomorphism classes of simplicial arrangements in the real projective plane with up to 27 lines. It turns out that Gr\"unbaums 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 Gr\"unbaums conjecture about unstretchable arrangements with at most 16 lines, and prove the conjecture that any simplicial arrangement with at most 14 pseudolines is stretchable.
Cite
@article{arxiv.1108.3000,
title = {Simplicial arrangements with up to 27 lines},
author = {Michael Cuntz},
journal= {arXiv preprint arXiv:1108.3000},
year = {2011}
}
Comments
18 pages, 5 figures, 3 tables