3 problems

Let $Pr(n)$ and $Ar(n)$ denote uniform prisms and antiprisms, respectively, with $n$-gon bases. Let $N_{Pr(n)}$ and $N_{Ar(n)}$ be the corresponding partition counts, and suppose t…

Let $N(d,k,t)$ denote the least integer such that every set of $N(d,k,t)$ points in general position in $\mathbb{R}^d$ admits a partition into $k$ parts whose convex hulls intersec…

Let $N(d,k,t)$ denote the least integer such that every set of $N(d,k,t)$ points in general position in $\mathbb{R}^d$ admits a partition into $k$ parts whose convex hulls intersec…