On the Ehrhart Polynomial of Minimal Matroids

We provide a formula for the Ehrhart polynomial of connected matroid size $n$ and rank $k$ with least number bases, also known as minimal matroid. prove that their polytopes are positive $h^*$-real-rooted (and hence unimodal). operation circuit-hyperplane relaxation relates matroids subdivisions, preserves positivity. state two conjectures: indeed all $h^*$-real-rooted, coefficients fixed cardinality bounded by those corresponding uniform