Discrete Math Seminar: Ehrhart theory of paving and panhandle matroid polytopes

Ehrhart theory is a topic in geometric combinatorics which involves the enumeration of lattice points in integral dilates of polytopes. We introduce panhandle matroids, which generalize the previously studied uniform matroids and minimal connected matroids. We provide a formula for the Ehrhart polynomial of the matroid polytope of panhandle and paving matroids. We also make substantial progress toward proving that the coefficients of the Ehrhart polynomials for panhandle matroids are positive, and we reduce this problem to a purely combinatorial enumeration problem.