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I previously posted this on MathSE and am now trying here. I have the following situation, as shown in the following diagram: $W=\{w_i\}_{i=1..|W|}$ is a set of vertices (show in diagram in blue) ...

Suppose that $P$ is a polyhedron represented by $$P:=\{x \in \mathbb{R}^n: A x \le b \} \text{ for }A \in \mathbb{R}^{m\times n},\ b \in \mathbb{R}^m,$$ and $P$ contains interior points. Moreover, the ...

Let $X \subset \mathbb{Z}^n$ be the set of integer-valued vectors satisfying a system of linear constraints. We can suppose that $X$ is the set of integral points in a given polyhydral set $Y \subset \...