All Questions

Assume we have sets of the form $$ M_j = \{x\in\mathbb{R}^d : f_j(x) \le 0,x \ge 0\} $$ where $x\ge 0$ means $x_i \ge 0 \quad \forall i=1,\dots, d$. Goal I am looking for an (explicit) representation ...

Consider polytopes $$A_1[x_{1,1},\dots,x_{1,m_1},z_{1}]'\leq b_1$$ $$A_2[x_{2,1},\dots,x_{2,m_2},z_{2}]'\leq b_2$$ $$B[z_{1},z_{2},z]'\leq c$$ having vertex count $v_1,v_2$ and $v$ respectively. We ...

Let us define the $n$-permutohedron $P_n$ as the set of all $x\in\mathbb{Q}^n$ such that $$\sum_{i=1}^n x_i = \binom{n{+}1}{2}\ \ \ \land\ \ \ \forall\,\text{nonempty}\ S\subsetneq\mathbb{N}_n\colon\ ...