10 citations · 22 across the 7 of their papers we have counts for
8 papers
Minkowski sum of a Voronoi parallelotope and a segment
Robert Erdahl, Viacheslav Grishukhin
By a {\em Voronoi parallelotope} we mean a parallelotope determined by a non-negative quadratic form . It was studied by Voronoi in his famous memoir. For a set of vector…
Perfect Delaunay Polytopes in Low Dimensions
Mathieu Dutour, Robert Erdahl, Konstantin Rybnikov
A lattice Delaunay polytope is known as perfect if the only ellipsoid, that can be circumscribed about it, is its Delaunay sphere. Perfect Delaunay polytopes are in one-to-one corr…
Perfect Delaunay Polytopes and Perfect Quadratic Functions on Lattices
Robert Erdahl, Andrei Ordine, Konstantin Rybnikov
A polytope whose vertices belong to a lattice of rank is Delaunay if there is a circumscribing -dimensional ellipsoid, , with interior free of lattice points so that…
Supertopes
Robert Erdahl, Konstantin Rybnikov
A perfect (Delaunay) ellipsoid is an ellipsoid in n-dimensional Euclidean space that does not contain integral points in its interior, but is uniquely defined by integral points th…
Perfect Delaunay Polytopes and Perfect Inhomogeneous Forms
Robert Erdahl, Andrei Ordine, Konstantin Rybnikov
A lattice Delaunay polytope D is called perfect if it has the property that there is a unique circumscribing ellipsoid with interior free of lattice points, and with the surface co…
An Infinite Series of Perfect Quadratic Forms and Big Delaunay Simplexes in Z^n
Robert Erdahl, Konstantin Rybnikov
George Voronoi (1908-09) introduced two important reduction methods for positive quadratic forms: the reduction with perfect forms, and the reduction with L-type domains. A form is…