De Loera–Haws–Köppe positivity conjecture for matroid Ehrhart polynomials

Let $\mathsf{M}$ be a matroid, and let $\mathscr{P}(\mathsf{M})$ be its matroid base polytope. Denote by $\operatorname{ehr}(\mathscr{P}(\mathsf{M}),t)$ its Ehrhart polynomial. Ehrhart positivity conjecture. The polynomial $\operatorname{ehr}(\mathscr{P}(\mathsf{M}),t)$ has positive coefficients. This conjecture concerns lattice-point enumeration in dilations of matroid base polytopes; the paper presents it as an open conjecture and notes that related cases have been checked.