5 problems

Asymptotic Carathéodory-rank conjecture. The ratio $\operatorname{CR}(d)/d$ is monotonically converging to $2$ as $d\to\infty$. The source records a counterexample to the integral…

An integral cyclic polytope is a cyclic polytope with integral vertices. A lattice polytope is very ample when its associated semigroup is generated up to saturation in the usual t…

Let $C_d(\tau_1,\dotsc,\tau_n)$ and $C_d(\tau_1',\dotsc,\tau_n')$ be integral cyclic polytopes, and let $\Delta_{ij}$ denote the corresponding gaps used in the source. Assume that…

Let $C_4(\tau_1,\tau_2,\dotsc,\tau_n)$ be a cyclic polytope, and write $\Delta_{ij}=\tau_j-\tau_i$ for $i<j$. A lattice polytope is normal when every lattice point in every positiv…

A cyclic polytope is the convex hull of points on the moment curve; here, normal means that every lattice point in every positive dilate is a sum of lattice points of the polytope.…