On a Simple Connection Between $\Delta$-modular ILP and LP, and a New Bound on the Number of Integer Vertices

D. V. Gribanov, D. S. Malyshev, I. A. Shumilov

Let $A\in Z^{m\times n}$, $rank(A)=n$, $b\in Z^m$, and $P$ be an $n$-dimensional polyhedron, induced by the system $Ax\le b$. It is a known fact that if $F$ is a $k$-face o…