The diameter of lattice zonotopes

We establish sharp asymptotic estimates for the diameter of primitive zonotopes when their dimension is fixed and the number of their generators grows large. We also prove that, for infinitely many integers kk, the largest possible diameter δz(d,k)\delta _z(d,k) of a lattice zonotope contained in the hypercube [0,k]d[0,k]^d is uniquely achieved by a primitive zonotope. We obtain, as a consequence, that δz(d,k)\delta _z(d,k) grows like …