10 papers · 1 filter
Is there a smooth lattice polytope which does not have the integer decomposition property?
Johannes Hofscheier, Alexander Kasprzyk
We introduce Tadao Oda's famous question on lattice polytopes which was originally posed at Oberwolfach in 1997 and, although simple to state, has remained unanswered. The question…
Examples of IDP lattice polytopes with non-log-concave -vector
Johannes Hofscheier, Vadym Kurylenko, Benjamin Nill
Lattice polytopes are called IDP polytopes if they have the integer decomposition property, i.e., any lattice point in a th dilation is a sum of lattice points in the polyto…
Classification and Ehrhart Theory of Denominator 2 Polygons
Girtrude Hamm, Johannes Hofscheier, Alexander Kasprzyk
We present an algorithm for growing the denominator polygons containing a fixed number of lattice points and enumerate such polygons containing few lattice points for small …
Machine Learning the Dimension of a Polytope
Tom Coates, Johannes Hofscheier, Alexander Kasprzyk
We use machine learning to predict the dimension of a lattice polytope directly from its Ehrhart series. This is highly effective, achieving almost 100% accuracy. We also use machi…
Polytopes and Machine Learning
Jiakang Bao, Yang-Hui He, Edward Hirst +3
We introduce machine learning methodology to the study of lattice polytopes. With supervised learning techniques, we predict standard properties such as volume, dual volume, reflex…
Generalized flatness constants, spanning lattice polytopes, and the Gromov width
Gennadiy Averkov, Johannes Hofscheier, Benjamin Nill
In this paper we motivate some new directions of research regarding the lattice width of convex bodies. We show that convex bodies of sufficiently large width contain a unimodular…