Totally Splittable Polytopes

Totally Splittable Polytopes

Matching polytopes, toric geometry, and the totally non-negative Grassmannian

In this paper we use toric geometry to investigate the topology of the totally non-negative part of the Grassmannian, denoted (Grk,n)≥0. This is a cell complex whose cells G can be parameterized in terms of the combinatorics of plane-bipartite graphs G. To each cell G we associate a certain polytope P(G). The polytopes P(G) are analogous to the well-known Birkhoff polytopes, and we describe the...

Isolating a Vertex via Lattices: Polytopes with Totally Unimodular Faces

We deterministically construct quasi-polynomial weights in quasi-polynomial time, such that in a given polytope with totally unimodular constraints, one vertex is isolated, i.e., there is a unique minimum weight vertex. More precisely, the property that we need is that every face of the polytope lies in an affine space defined by a totally unimodular matrix. This derandomizes the famous Isolati...

Splittable metamorphic carrier robots

Metamorphic modular robots are versatile systems composed of a set of independent modules. These modules are able to deliberately change their overall topology in order to adapt to new circumstances, perform new tasks, or recover from damage. The modules considered in this paper are cubic shapes, and we assume that each of them has a separate computational resources and it is equipped with spec...

Splittable Triplewhist Tournament Designs

We show that Z-cyclic splittable triplewhist tournament designs exist for all primes of the form p = 8t + 1, t odd, except possibly p = 41.