89 citations · 735 across the 47 of their papers we have counts for
12 papers · 1 filter
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…
Quasi-period collapse for duals to Fano polygons: an explanation arising from algebraic geometry
Alexander M. Kasprzyk, Ben Wormleighton
The Ehrhart quasi-polynomial of a rational polytope is a fundamental invariant counting lattice points in integer dilates of . The quasi-period of this quasi-polynomial divi…
Three-dimensional lattice polytopes with two interior lattice points
Gabriele Balletti, Alexander M. Kasprzyk
We classify the three-dimensional lattice polytopes with two interior lattice points. Up to unimodular equivalence there are 22,673,449 such polytopes. This classification allows u…
On the maximum dual volume of a canonical Fano polytope
Gabriele Balletti, Alexander M. Kasprzyk, Benjamin Nill
We give an upper bound on the volume vol(P*) of a polytope P* dual to a d-dimensional lattice polytope P with exactly one interior lattice point, in each dimension d. This bound, e…
Ehrhart polynomial roots of reflexive polytopes
Gábor Hegedüs, Akihiro Higashitani, Alexander Kasprzyk
Recent work has focused on the roots z of the Ehrhart polynomial of a lattice polytope P. The case when Re(z) = -1/2 is of particular interest: these polytopes satisfy Golyshev's "…