Some six-dimensional rigid forms

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

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Metric Geometry, Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/95910

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0401191
 http://arxiv.org/abs/math/0401191
 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).

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