5 problems

Castillo–Liu conjecture. Every integral generalized permutohedron $\mathscr{P}$ is Ehrhart positive.

An integral generalized permutohedron is a polytope whose edges are parallel to vectors $e_i-e_j$; equivalently, it is a base polytope of a discrete polymatroid. A polytope is Ehrh…

Let $I$ and $J$ be sets indexing the $u$-variables of $\mathscr{P}_n$, and let $h_{I,n}$ denote the correction term in the equation for $u_I$. Compatibility-degree and positivity c…

Let $\mathscr{P}_n$ be the generalized permutohedron with variables $u_I$ indexed by the relevant sets $I$. For sets $I$ and $J$, write $J||I$ for their positive integer compatibil…

Berline–Vergne positivity conjecture. The value $\alpha^{\textsc{bv}}(F,P)$ is positive for every face $F\subset P$. Equivalently, $\alpha^{\textsc{bv}}$ is positive on every cone…