Classification of eight-dimensional perfect forms-Reference-Cited by-同舟云学术

Classification of eight-dimensional perfect forms

Published:2007-04-11 Issue:3 Volume:13 Page:21-32
ISSN:1079-6762
Container-title:Electronic Research Announcements of the American Mathematical Society
language:en
Short-container-title:Electron. Res. Announc. Amer. Math. Soc.

Author:

Sikirić Mathieu,Schürmann Achill,Vallentin Frank

Abstract

In this paper, we classify the perfect lattices in dimension 8 8 . There are 10916 10916 of them. Our classification heavily relies on exploiting symmetry in polyhedral computations. Here we describe algorithms making the classification possible.

Publisher

American Mathematical Society (AMS)

Subject

General Mathematics

Reference52 articles.

1. On the density of a lattice covering for 𝑛=11 and 𝑛=14;Anzin, M. M.;Tr. Mat. Inst. Steklova,2002

2. Lie Groups: History, Frontiers and Applications, Vol. IV;Ash, A.,1975

3. [Av93]lrs D. Avis, A C-implementation of the reverse search vertex enumeration algorithm, School of Computer Science, McGill University, Montreal, Canada 1993, http://www-cgrl.cs.mcgill.ca/˜avis/C/lrs.html.

4. On the graph structure of convex polyhedra in 𝑛-space;Balinski, M. L.;Pacific J. Math.,1961

5. [Ba96]baril J-L. Baril, Autour de l’algorithme de Voronoi: Construction de réseaux Euclidiens, Thèse, Bordeaux (1996).

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