Some six-dimensional rigid forms
| dc.creator | Dutour, Mathieu | |
| dc.creator | Vallentin, Frank | |
| dc.date | 2004-01-16 | |
| dc.date | 2005-01-04 | |
| dc.date.accessioned | 2026-07-07T06:22:26Z | |
| dc.date.available | 2026-07-07T06:22:26Z | |
| dc.description | 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. | |
| dc.description | 8 pages, a few details added, to appear in proceedings of Voronoi conference on analytic number theory and spatial tessellations | |
| dc.identifier | https://arxiv.org/abs/math/0401191 | |
| dc.identifier | http://arxiv.org/abs/math/0401191 | |
| dc.identifier | pages 102-108 in Voronoi's Impact on Modern Science, Book 3 (H. Syta, A. Yurachivsky, P. Engel eds.; Institute of Math., Kyiv 2005 = Vol.55 of Proc. Inst. Math. Nat. Acad. Sci. Ukraine). | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95910 | |
| dc.subject | Metric Geometry | |
| dc.subject | Combinatorics | |
| dc.title | Some six-dimensional rigid forms | |
| dc.type | text |