6 papers · 1 filter
A very ample lattice polytope with a non-unimodal -vector
Johannes Hofscheier, Vadym Kurylenko, Benjamin Nill
Lattice polytopes are called very ample if for every sufficiently large every lattice point of height in the cone over the lattice polytope is the sum of lattice points…
Lattice polytopes of large width have real-rooted Ehrhart -polynomials
Benjamin Nill
In this note we prove that in fixed dimension the Ehrhart -polynomial of a lattice polytope of sufficiently large lattice width is real-rooted. In particular, this implies str…
Preserving Hodge Vectors of Lattice Polytopes
Vadym Kurylenko, Benjamin Nill
Given lattice polytopes contained in a -dimensional subspace and a -dimensional lattice polytope , we co…
Unimodular polytopes and column number bounds on polytopal totally unimodular matrices via Seymour's decomposition theorem
Benjamin Nill
We prove a sharp upper bound on the number of distinct columns of a totally unimodular matrix with column sums improving upon Heller's classical bound. The proof uses Seymour's…
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…
Empty simplices of large width
Joseph Doolittle, Lukas Katthän, Benjamin Nill +1
An empty simplex is a lattice simplex in which vertices are the only lattice points. We show two constructions leading to the first known empty simplices of width larger than their…