Some sixdimensional rigid forms
Abstract
One can always decompose DirichletVoronoi polytopes of lattices nontrivially into a Minkowski sum of DirichletVoronoi 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 Ltype 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2004
 arXiv:
 arXiv:math/0401191
 Bibcode:
 2004math......1191D
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Combinatorics
 EPrint:
 8 pages, a few details added, to appear in proceedings of Voronoi conference on analytic number theory and spatial tessellations