3 problems

Let $T$ be a lattice tetrahedron with exactly $k$ interior lattice points. In a minimal direction for its lattice width, consider the consecutive lattice planes meeting $T$. Lattic…

Let $\mathscr{S}_k^3$ denote the family of clean lattice tetrahedra in $\mathbb{R}^3$ with $k$ interior lattice points, let $\operatorname{Vol}(T)$ denote the normalized volume, an…

Let $\mathscr{S}_k^3$ denote the family of clean lattice tetrahedra in $\mathbb{R}^3$ with $k$ interior lattice points, and let $\operatorname{Vol}(T)$ denote the normalized volume…