Some six-dimensional rigid forms
摘要
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.
引用
@article{arxiv.math/0401191,
title = {Some six-dimensional rigid forms},
author = {Mathieu Dutour and Frank Vallentin},
journal= {arXiv preprint arXiv:math/0401191},
year = {2007}
}
备注
8 pages, a few details added, to appear in proceedings of Voronoi conference on analytic number theory and spatial tessellations