1 citations · 3 across the 3 of their papers we have counts for
5 papers
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…
On locally convex PL-manifolds and fast verification of convexity
Konstantin Rybnikov
We show that a realization of a closed connected PL-manifold of dimension n-1 in Euclidean n-space (n>2) is the boundary of a convex polyhedron if and only if the interior of each…
Fast Verification of Convexity of Piecewise-linear Surfaces
Konstantin Rybnikov
We show that a realization of a closed connected PL-manifold of dimension n-1 in n-dimensional Euclidean space (n>2) is the boundary of a convex polyhedron (finite or infinite) if…
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…
Voronoi-Dickson Hypothesis on Perfect Forms and L-types
Robert Erdahl, Konstantin Rybnikov
George Voronoi (1908, 1909) introduced two important reduction methods for positive quadratic forms: the reduction with perfect forms, and the reduction with L-type domains, often…