Sublattices of certain Coxeter lattices

Anne-Marie Bergé[1]; Jacques Martinet[1]

  • [1] Université Bordeaux 1 351, cours de la Libération 33451 Talence Cedex, France

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 2, page 455-465
  • ISSN: 1246-7405

Abstract

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

How to cite

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Bergé, Anne-Marie, and Martinet, Jacques. "Sublattices of certain Coxeter lattices." Journal de Théorie des Nombres de Bordeaux 17.2 (2005): 455-465. <http://eudml.org/doc/249427>.

@article{Bergé2005,
abstract = {In this paper, we describe the sublattices of some lattices, extending previous results of [Ber]. Our description makes intensive use of graphs.},
affiliation = {Université Bordeaux 1 351, cours de la Libération 33451 Talence Cedex, France; Université Bordeaux 1 351, cours de la Libération 33451 Talence Cedex, France},
author = {Bergé, Anne-Marie, Martinet, Jacques},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Eutactic lattices; spherical designs; kissing number; bipartite graphs; Coxeter lattice; eutactic lattice; spherical design; bipartite graph},
language = {eng},
number = {2},
pages = {455-465},
publisher = {Université Bordeaux 1},
title = {Sublattices of certain Coxeter lattices},
url = {http://eudml.org/doc/249427},
volume = {17},
year = {2005},
}

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
PB - Université Bordeaux 1
VL - 17
IS - 2
SP - 455
EP - 465
AB - In this paper, we describe the sublattices of some lattices, extending previous results of [Ber]. Our description makes intensive use of graphs.
LA - eng
KW - Eutactic lattices; spherical designs; kissing number; bipartite graphs; Coxeter lattice; eutactic lattice; spherical design; bipartite graph
UR - http://eudml.org/doc/249427
ER -

References

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  1. A.-M. Bergé, On certain Coxeter lattices without perfect sections. J. Algebraic Combinatorics 20 (2004), 5–16. Zbl1054.05093MR2104817
  2. A.-M. Bergé, J. Martinet, Symmetric Groups and Lattices. Monatsh. Math. 140 (2003), 179–195. Zbl1132.11329MR2017668
  3. B. Bollobás, Modern graph theory. Graduate texts in Mathematics 184, Springer-Verlag, Heidelberg, 1998. Zbl0902.05016MR1633290
  4. H.S.M. Coxeter, Extreme forms. Canad. J. Math. 3 (1951), 391–441. Zbl0044.04201MR44580
  5. J. Martinet, Perfect Lattices in Euclidean Spaces. Grundlehren 327, Springer-Verlag, Heidelberg, 2003. Zbl1017.11031MR1957723
  6. 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. Zbl1139.11320

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