Benjamin Nill

collaborators

4 papers

math.CO2026

Lattice polytopes of large width have real-rooted Ehrhart $h^{*}$ -polynomials

Benjamin Nill

In this note we prove that in fixed dimension the Ehrhart $h^{*}$ -polynomial of a lattice polytope of sufficiently large lattice width is real-rooted. In particular, this implies str…

math.CO2026

Preserving Hodge Vectors of Lattice Polytopes

Vadym Kurylenko, Benjamin Nill

Given lattice polytopes $P_{1}, \dots, P_{k}$ contained in a $k$ -dimensional subspace $U \subseteq R^{d}$ and a $d$ -dimensional lattice polytope $Q \subset R^{d}$ , we co…

math.CO2026

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 $1$ improving upon Heller's classical bound. The proof uses Seymour's…

math.CO2025

Examples of IDP lattice polytopes with non-log-concave $h^{*}$ -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 $k$ th dilation is a sum of $k$ lattice points in the polyto…

Lattice polytopes of large width have real-rooted Ehrhart h∗-polynomials

Preserving Hodge Vectors of Lattice Polytopes

Unimodular polytopes and column number bounds on polytopal totally unimodular matrices via Seymour's decomposition theorem

Examples of IDP lattice polytopes with non-log-concave h∗-vector

Lattice polytopes of large width have real-rooted Ehrhart $h^{*}$ -polynomials

Examples of IDP lattice polytopes with non-log-concave $h^{*}$ -vector