2 papers
math.CO2025
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…
math.CO2025
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…