32 citations · 52 across the 7 of their papers we have counts for
7 papers
Generalized Perfect Matrices
Alexander Oertel, Achill Schürmann
We generalize Voronoi's theory of perfect quadratic forms to generalized copositive matrices over a full-dimensional closed convex cone K, by introducing a K-copositive minimum and…
On Computing the Copositive Minimum and its Representatives
Alexander Oertel, Achill Schürmann
Computing the copositive minimum of a strictly copositive quadratic form is a natural generalization of computing the arithmetical minimum of a positive definite one. In this paper…
Rational factorizations of completely positive matrices
Mathieu Dutour Sikirić, Achill Schürmann, Frank Vallentin
In this note it is proved that every rational matrix which lies in the interior of the cone of completely positive matrices also has a rational cp-factorization.
Exploiting Symmetries in Polyhedral Computations
Achill Schürmann
In this note we give a short overview on symmetry exploiting techniques in three different branches of polyhedral computations: The representation conversion problem, integer linea…
Strict Periodic Extreme Lattices
Achill Schürmann
A lattice is called periodic extreme if it cannot locally be modified to yield a better periodic sphere packing. It is called strict periodic extreme if its sphere packing density…
Exploiting Polyhedral Symmetries in Social Choice
Achill Schürmann
A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting…
Perfect, strongly eutactic lattices are periodic extreme
Achill Schürmann
We introduce a parameter space for periodic point sets, given as unions of translates of point lattices. In it we investigate the behavior of the sphere packing density functio…