Voronoi-Dickson Hypothesis on Perfect Forms and L-types

Details Voronoi-Dickson Hypothesis on Perfect Forms and L-types Voronoi-Dickson Hypothesis on Perfect Forms and L-types

2001-12-11

arxiv.org/abs/math/0112097v1

Mathematics

Number Theory

Short Version

Scientific paper

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 called domains of Delaunay type. The first method is important in studies of dense lattice packings of spheres. The second method provides the key tools for finding the least dense lattice coverings with equal spheres in lower dimensions. In his investigations Voronoi heavily relied on that in dimensions less than 6 the partition of the cone of positive quadratic forms into L-types refines the partition of this cone into perfect domains. Voronoi conjectured implicitely and Dickson (1972) explicitely that the L-partition is always a refinement of the partition into perfect domains. This was proved for n =< 5 (Voronoi, Delaunay, Ryshkov, Baranovskii). We show that Voronoi-Dickson conjecture fails already in dimension 6.

Affiliated with

Also associated with

No associations

Rating

Voronoi-Dickson Hypothesis on Perfect Forms and L-types does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Voronoi-Dickson Hypothesis on Perfect Forms and L-types, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Voronoi-Dickson Hypothesis on Perfect Forms and L-types will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-140165