4 papers
On Lattice Diameter Segments and A Discrete Borsuk Partition Problem
Anouk E. Brose, Jesús A. De Loera, Gyivan Lopez-Campos +1
The lattice diameter of a bounded set measures the maximal number of lattice points in a segment whose endpoints are lattice points in . Such a segment…
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. RamÃrez AlfonsÃn
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 se…
Matroids, intersecting bases, and Borsuk property
Gyivan López-Campos, Frédéric Meunier, Jorge L. RamÃrez AlfonsÃn
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…