Some six-dimensional rigid forms

Details Some six-dimensional rigid forms Some six-dimensional rigid forms

2004-01-16

arxiv.org/abs/math/0401191v3

pages 102-108 in Voronoi's Impact on Modern Science, Book 3 (H. Syta, A. Yurachivsky, P. Engel eds.; Institute of Math., Kyiv

Mathematics

Metric Geometry

8 pages, a few details added, to appear in proceedings of Voronoi conference on analytic number theory and spatial tessellatio

Scientific paper

One can always decompose Dirichlet-Voronoi polytopes of lattices non-trivially into a Minkowski sum of Dirichlet-Voronoi polytopes of rigid lattices. In this report we show how one can enumerate all rigid positive semidefinite quadratic forms (and thereby rigid lattices) of a given dimension d. By this method we found all rigid positive semidefinite quadratic forms for d = 5 confirming the list of 7 rigid lattices by Baranovskii and Grishukhin. Furthermore, we found out that for d <= 5 the adjacency graph of primitive L-type domains is an infinite tree on which GL_d(Z) acts. On the other hand, we demonstrate that in d = 6 we face a combinatorial explosion.

Affiliated with

Also associated with

No associations

Rating

Some six-dimensional rigid forms 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 Some six-dimensional rigid forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some six-dimensional rigid forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-585651