On the integer points in a lattice polytope: n-fold Minkowski sum and boundary

In this article we compare the set of integer points in the homothetic copy nΠ of a lattice polytope Π⊆ᵈ with the set of all sums x₁+⋯+xn with x₁,...,xn∈ Π∩ᵈ and n∈. We give conditions on the polytope Π under which these two sets coincide and we discuss two notions of boundary for subsets of ᵈ or, more generally, subsets of a finitely generated discrete group.

Subjects

Metric Geometry