64 citations · 449 across the 29 of their papers we have counts for
14 papers · 1 filter
Perfect Copositive Matrices
Valentin Dannenberg, Achill Schürmann
In this paper we give a first study of perfect copositive matrices. They can be used to find rational certificates for completely positive matrices. We describe simila…
Local Energy Optimality of Periodic Sets
Renaud Coulangeon, Achill Schürmann
We study the local optimality of periodic point sets in for energy minimization in the Gaussian core model, that is, for radial pair potential functions $f_c(r)=e^{-…
Local Formulas for Ehrhart Coefficients from Lattice Tiles
Maren H. Ring, Achill Schürmann
As shown by McMullen in 1983, the coefficients of the Ehrhart polynomial of a lattice polytope can be written as a weighted sum of facial volumes. The weights in such a local formu…
Equivalence of Lattice Orbit Polytopes
Frieder Ladisch, Achill Schürmann
Let be a finite permutation group acting on by permuting coordinates. A core point (for ) is an integral vector such that the convex hull…
The complete classification of five-dimensional Dirichlet-Voronoi polyhedra of translational lattices
Mathieu Dutour Sikirić, Alexey Garber, Achill Schürmann +1
In this paper we report on the full classification of Dirichlet-Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. We obtain a complete list of…
On Lattice-Free Orbit Polytopes
Katrin Herr, Thomas Rehn, Achill Schürmann
Given a permutation group acting on coordinates of , we consider lattice-free polytopes that are the convex hull of an orbit of one integral vector. The vertices of s…