Computer solution of the almost empty hexagon problem (Q650447)

For any integer \(n\geq 3\) and \(k\geq 0\), let \(h(n,k)\) denote the smallest positive integer such that any set of at least \(h(n,k)\) points in general position in the plane has a subset of \(n\) points forming a convex \(n\)-gon, whose interior contains at most \(k\) of the points. The paper evaluates \(h(n,k)\) exactly for all \(n\leq 6\), except \(h(6,0)\), using a computer. These results refute a claim from the paper [\textit{H. Nyklová}, Stud. Sci. Math. Hung. 40, No. 3, 269--286 (2003; Zbl 1050.52006)].