On a characterization of lattice cubes via discrete isoperimetric inequalities (Q2684893)

A lattice cube is the intersection of an \(n\)-dimensional cube \([a, b] \in \mathbb R^n\) with the integer lattice \(\mathbb Z^n\). The authors obtain a characterization of lattice cubes as the only extremal sets for which several discrete isoperimetric-type inequalities associated with the \(L_\infty\) norm are sharp (including the well-known theorem by Radcliffe and Veomett). Additionally the authors provide a new isoperimetric inequality for the lattice point enumerator that generalizes previous result.