The metric polytope is a (;)-dimensional convex polytope defined by its 4 (~) facets. The vertices
of the metric polytope are known only up to n= 6, for n= 7 they number more than 60000. …

Counting the types of squares rather than their occurrences, we consider the problem of
bounding the number of distinct squares in a string. Fraenkel and Simpson showed in 1998 that …

We show that the largest possible diameter $${\delta(d,k)}$$ δ ( d , k ) of a d-dimensional
polytope whose vertices have integer coordinates ranging between 0 and k is at most $${kd - \…

A class of counting problems asks for the number of regions of a central hyperplane arrangement.
By duality, this is the same as counting the vertices of a zonotope. Efficient algorithms …

We introduce and study the problem of optimizing arbitrary functions over degree sequences
of hypergraphs and multihypergraphs. We show that over multihypergraphs the problem …

This paper presents an extension of a recently introduced multistage stochastic integer
model designed for optimizing the deployment of charging stations under uncertainty. A key …

Primitive zonotopes arise naturally in various research areas, such as discrete geometry,
combinatorial optimization, and theoretical physics. We provide geometric and combinatorial …

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 …

A point in the d‐dimensional integer lattice Z d $\mathbb {Z}^d$ is primitive when its coordinates
are relatively prime. Two primitive points are multiples of one another when they are …

We consider convex polyhedra with applications to well-known combinatorial optimization
problems: the metric polytope m n and its relatives. For n ≤ 6 the description of the metric …