The distribution of roots of Ehrhart polynomials for the dual of root polytopes of type \(C\) (Q6166668)

Consider an integer polytope of type \(C\) of dimension \(d\) and let \(C^\ast_d\) denotes the dual of the root polytope of such polytope. The authors provide an explicit formula for the values of the Ehrhart polynomial of \(C^\ast_d\) and prove that its roots have the same real part \(-1/2\). They also show that the Ehrhart polynomial of \(C^\ast_d\) satisfies the interlacing property (with respect to dimension \(d\)).