2 problems

Let ${\mathrm {PDS}}_4$ be the set of permutative doubly stochastic matrices of order $4$, and let $\Pi_3\setminus\Pi_4$ denote the part of the third-root polygon outside the fourt…

Let ${\mathrm {PDS}}_4$ be the set of permutative doubly stochastic matrices of order $4$, and let $\Pi_3$ and $\Pi_4$ be the convex hulls of the third and fourth roots of unity, r…