5 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…

Duong–author sharpness conjecture. These bounds are sharp for all $k\ge 1$: the lower equality case is represented by $T_{3k,3k,3k+1}$, and the upper equality case by…

Let $T$ be a clean lattice tetrahedron, and let $i(T)$ denote its number of interior lattice points. Its lattice width is the minimum, over nonzero integer linear forms, of the num…

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…