4 papers · 1 filter
On Lattice Diameter Segments: Algorithms and Structure
Gennadiy Averkov, Anouk E. Brose, Jesús A. De Loera +2
The lattice diameter of a bounded set counts the maximal number of lattice points in a segment whose endpoints are lattice points in . Such a segment is…
Matroids, intersecting bases, and Borsuk property
Gyivan López-Campos, Frédéric Meunier, Jorge L. Ramírez Alfonsín
A subset of has the Borsuk property if it can be decomposed into at most parts of diameter smaller than . This is an important geometric property, inspir…
On the Number of Vertices in a Hyperplane Section of a Polytope
Jesús A. De Loera, Gyivan Lopez-Campos, Antonio J. Torres
We study the slices or sections of a convex polytope by affine hyperplanes. We present results on two key problems: First, we provide tight bounds on the maximum number of vertices…
Borsuk and Vázsonyi problems through Reuleaux polyhedra
Gyivan Lopez-Campos, Deborah Oliveros, Jorge L. Ramírez Alfonsín
The Borsuk conjecture and the Vázsonyi problem are two attractive and famous questions in discrete and combinatorial geometry, both based on the notion of diameter of a bounded set…