3 problems

Let $g_\mathrm{col}(n)$ denote the relevant extremal quantity for colored radial orderings of bichromatic sets of $2n$ points. Quadratic colored-ordering conjecture. … The paper no…

Let $S$ be a set of $n$ points in general position in the plane, meaning that no three points are collinear. General-position quartic lower-bound conjecture. $S$ has at least…

Let $g(n)$ denote the minimum number of distinct radial orderings determined by a set of $n$ points in strong general position in the plane. Quartic growth conjecture. … The paper…