5 papers
Central limit theorems for high dimensional lattice polytopes: cosmological polytopes
Torben Donzelmann, Martina Juhnke, Benedikt Rednoß +1
We study cosmological polytopes induced by Erdős--Rényi random graphs in a high-dimensional regime. These graph-based lattice polytopes form a natural model of random lattice polyt…
Central limit theorems for high dimensional lattice polytopes: symmetric edge polytopes
Torben Donzelmann, Martina Juhnke, Benedikt Rednoß +1
We investigate symmetric edge polytopes generated by Erdős--Rényi random graphs in a high-dimensional regime. These objects provide a natural and largely unexplored model of random…
On cosmological polytopes, their canonical forms and their duals
Anna Birkemeyer, Torben Donzelmann, Mieke Fink +1
We compute the canonical form of the cosmological polytope for any graph in terms of the dual of the shifted cosmological polytope in two different ways. On the way, we provide an…
Symmetric (co)homology polytopes
Torben Donzelmann, Thiago Holleben, Martina Juhnke
Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to a…
Crossing Numbers of Beyond Planar Graphs Re-revisited: A Framework Approach
Markus Chimani, Torben Donzelmann, Nick Kloster +3
Beyond planarity concepts (prominent examples include k-planarity or fan-planarity) apply certain restrictions on the allowed patterns of crossings in drawings. It is natural to as…