Simplicial arrangements with up to 27 lines

Details Simplicial arrangements with up to 27 lines Simplicial arrangements with up to 27 lines

2011-08-15

arxiv.org/abs/1108.3000v1

Mathematics

Combinatorics

18 pages, 5 figures, 3 tables

Scientific paper

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.

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