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.
@article{JTNB_2005__17_2_455_0, author = {Berg\'e, Anne-Marie and Martinet, Jacques}, title = {Sublattices of certain {Coxeter} lattices}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {455--465}, publisher = {Universit\'e Bordeaux 1}, volume = {17}, number = {2}, year = {2005}, doi = {10.5802/jtnb.501}, zbl = {1093.11050}, mrnumber = {2211301}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jtnb.501/} }
TY - JOUR AU - Bergé, Anne-Marie AU - Martinet, Jacques TI - Sublattices of certain Coxeter lattices JO - Journal de théorie des nombres de Bordeaux PY - 2005 SP - 455 EP - 465 VL - 17 IS - 2 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.501/ DO - 10.5802/jtnb.501 LA - en ID - JTNB_2005__17_2_455_0 ER -
%0 Journal Article %A Bergé, Anne-Marie %A Martinet, Jacques %T Sublattices of certain Coxeter lattices %J Journal de théorie des nombres de Bordeaux %D 2005 %P 455-465 %V 17 %N 2 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.501/ %R 10.5802/jtnb.501 %G en %F JTNB_2005__17_2_455_0
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
Cited by Sources: