Sublattices of certain Coxeter lattices
Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 2, pp. 455-465.

In this paper, we describe the sublattices of some lattices, extending previous results of [Ber]. Our description makes intensive use of graphs.

Dans cet article, nous décrivons les sous-réseaux de certains réseaux de Coxeter, prolongeant les résultats de [Ber]. Notre description utilise des graphes.

DOI: 10.5802/jtnb.501
Keywords: Eutactic lattices, spherical designs, kissing number, bipartite graphs
Bergé, Anne-Marie 1; Martinet, Jacques 1

1 Université Bordeaux 1 351, cours de la Libération 33451 Talence Cedex, France
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Bergé, Anne-Marie; Martinet, Jacques. Sublattices of certain Coxeter lattices. Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 2, pp. 455-465. doi : 10.5802/jtnb.501. http://www.numdam.org/articles/10.5802/jtnb.501/

[Ber] A.-M. Bergé, On certain Coxeter lattices without perfect sections. J. Algebraic Combinatorics 20 (2004), 5–16. | MR | Zbl

[B-M] A.-M. Bergé, J. Martinet, Symmetric Groups and Lattices. Monatsh. Math. 140 (2003), 179–195. | MR | Zbl

[Bo] B. Bollobás, Modern graph theory. Graduate texts in Mathematics 184, Springer-Verlag, Heidelberg, 1998. | MR | Zbl

[Cox] H.S.M. Coxeter, Extreme forms. Canad. J. Math. 3 (1951), 391–441. | MR | Zbl

[Mar] J. Martinet, Perfect Lattices in Euclidean Spaces. Grundlehren 327, Springer-Verlag, Heidelberg, 2003. | MR | Zbl

[Ven] B. Venkov, Réseaux et designs sphériques (notes by J. Martinet). In Réseaux euclidiens, designs sphériques et groupes, L’Ens. Math., Monographie 37, J. Martinet ed., Genève (2001), 10–86. | Zbl

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