Primitive Zonotopes

Abstract

We introduce and study a family of polytopes which can be seen as a generalization of the permutahedron of type $B_d$. We highlight connections with the largest possible diameter of the convex hull of a set of points in dimension $d$ whose coordinates are integers between $0$ and $k$, and with the computational complexity of multicriteria matroid optimization.

arXiv commentThe title was slightly modified, and the determination of the computational complexity of multicriteria matroid optimization was added