89 citations · 338 across the 44 of their papers we have counts for
53 papers
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…
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…
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…
Thin polytopes: Lattice polytopes with vanishing local -polynomial
Christopher Borger, Andreas Kretschmer, Benjamin Nill
In this paper we study the novel notion of thin polytopes: lattice polytopes whose local -polynomials vanish. The local -polynomial is an important invariant in modern Eh…