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math.MG2026
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…
math.MG2012
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…
math.MG2008★ 12 cited
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…