3 problems

Dirac's conjecture. There is a constant $c>0$ such that some point of $S$ is incident to at least $c n$ lines determined by $S$.

Dirac--Goodman--Pollack conjecture. There is a constant $c>0$ such that

Let $\mathcal{A}$ be an arrangement consisting of $n$ pseudolines, and let $t^\mathcal{A}_2$ denote its number of double points. Its characteristic polynomial $\chi(\mathcal{A},t)$…