4 problems

For any $(v_0,v)\in\mathbb{R}^{n+1}$, let $\text{E-CG}(v_0,v)$ denote the corresponding Eigen-CG inequality, and let BH inequalities denote the Boros–Hammer inequalities. Nonnegati…

Let $k\in\mathbb{N}$ be fixed. For a rational polyhedron $P\subseteq\mathbb{R}^n$, define the $k$-dimensional projection closure by … where $\mathcal{L}_k$ is the family of $k$-dim…

Let $k\geq 3$ and $n\geq k$. For a rational polyhedron $P\subseteq\mathbb{R}^n$, let $\mathcal{H}_k(P)$ be its $k$-halfspace closure, and let … where $\mathcal{L}_k$ is the family…

Let $k\in\mathbb{N}$ be fixed. For a rational polyhedron $P$, define the $k$-halfspace closure by … where $Q_I$ denotes the integer hull of $Q$. Polyhedrality conjecture for the…