Simplicial arrangements with up to 27 lines

TL;DR

This paper classifies all simplicial arrangements with up to 27 lines in the real projective plane, completing Gr"unbaum's catalogue except for four new arrangements, and resolves conjectures about stretchability of arrangements.

Contribution

It provides a complete classification of simplicial arrangements up to 27 lines and disproves and proves key conjectures related to their stretchability.

Findings

Complete classification of arrangements up to 27 lines

Disproved Gr"unbaum's conjecture on unstretchable arrangements with ≤16 lines

Proved that arrangements with ≤14 pseudolines are stretchable

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.