3 problems

Let $P_n$ be the integral polytope of real $n\times n$ doubly stochastic matrices, and let $h_{P_n}^*(x)$ be its Ehrhart $h^*$-polynomial. Stanley's conjecture. The polynomial…

Let $\Omega_n$ be the Birkhoff polytope, $J_n$ the matrix whose entries are all $1/n$, and let $R_p(\Omega_n)$ denote the Chebyshev radius of $\Omega_n$ with respect to the operato…

Let ${\mathcal U}_4$ be the set of unistochastic matrices of order $4$, and let ${\mathcal B}_4$ be the Birkhoff polytope of doubly stochastic matrices of order $4$. Star-shapednes…