13 problems

Let $B_n$ be the number of non-isomorphic pseudoline arrangements of order $n$, and let $b_n:=\log_2(B_n)$. Knuth's upper-bound conjecture. … This conjecture concerns the asymptoti…

Blue-polygon bichromatic-face conjecture. Given a blue $k$-gon $P$ with at least $k-4$ red pseudolines passing through, there exists a bichromatic triangle or quadrangle on its ins…

Triangle-pseudoline incidence graph conjecture. The triangle-pseudoline incidence graph of a pseudoline arrangement is connected.

Björner–Las Vergnas–Sturmfels–White–Ziegler conjecture. Every bicolored arrangement has a bichromatic triangle.

Let $\mathcal{L}\subset\mathbb{RP}^2$ be an essential pseudoline arrangement, and let $M$ be its matroid. Let $Q$ be the Hirzebruch quadratic form of $M$, and let the semistable co…

Let $\mathcal{A}$ be an arrangement of pseudolines, and let $\operatorname{mx}(\mathcal{A})$ denote the maximum number of crossings on any pseudoline. A coloring of the crossings i…

Consider an arrangement of pseudolines with at least three lines, and color each pseudoline with one of two colors. The bicoloring is non-monochromatic if both colors occur, and a…

For a finite set of points in the plane, consider every line determined by at least two points of the set, and compare the numbers of points on its two sides. Stretchable-configura…

Exit-edge witness conjecture. Knowing all exit edges and their witnesses, equivalently all triangular cells and their orientations in the dual line arrangement, is sufficient to de…

Stretchability conjecture. Every simplicial arrangement with at most $14$ pseudolines is stretchable.

Grünbaum's conjecture. Up to isomorphism, there are only $5$ simplicial unstretchable arrangements of $15$ or $16$ pseudolines.

Non-flipping common contacts conjecture. The shortest path in the flip graph $G({\mathcal S})$ between two pseudoline arrangements $\Lambda$ and $\Lambda'$ supported by…

A simple drawing is extendible if its edges are contained in a pseudoline arrangement: each edge lies on a simple unbounded curve, and any two such curves intersect at most once. A…