De Loera et al.'s Ehrhart positivity conjecture for matroid polytopes

Let $M$ be a matroid, and let $\mathscr{P}(M)$ denote its basis polytope. Its Ehrhart polynomial is the polynomial counting lattice points in integer dilations of $\mathscr{P}(M)$. De Loera et al.'s conjecture. The coefficients of the Ehrhart polynomial of $\mathscr{P}(M)$ are positive. This conjecture was posed for matroid basis polytopes and is motivated by Ehrhart-positivity questions in combinatorics. The paper proves the assertion for all hypersimplices, which are the basis polytopes of uniform matroids; the general matroid case is not resolved here.