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A generalization of some lattices of Coxeter

Published online by Cambridge University Press:  26 February 2010

Anne-Marie Bergé  and
Jacques Martinet
Anne-Marie Bergé
Affiliation:
Inst. Math., Université Bordeaux 1, 351, U. S. A., and cours de la Libération, 33405 Talence cedex, France, E-mail: berge@math.u-bordeaux.fr
Jacques Martinet
Affiliation:
Inst. Math., Université Bordeaux 1, 351, cours de la Libération, 33405 Talence cedex, France, E-mail: martinet@math.u-bordeaux.fr
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Abstract

This paper introduces a wide generalization of a family of integral lattices defined by Coxeter, which share with the Coxeter lattices the following properties: they are perfect, often with an odd minimum, and have no non-trivial perfect sections with the same minimum.

Type
Research Article
Information
Mathematika , Volume 51 , Issue 1-2 , December 2004 , pp. 49 - 61
Copyright
Copyright © University College London 2004

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References

[Bc-V]Bacher, R. and Venkov, B.. Réseaux entiers unimodulaires sans racincs en dimension 27 et 28. In Réseaux Euclidiens, Designs Spheriques et Groupes (ed. Martinet, J.), L 'Ens. Math., Monographie 37, Genéve (2001), 212–267.Google Scholar
[Bt-M]Batut, C. and Martinet, J.. A Catalogue of Perfect Lattices, http://www.math.ubordeaux. fr/~martinetGoogle Scholar
[Be]Berge, A.-M.. On certain Coxeter lattices without perfect sections. J. Algebntu Combinatorics 20 (2004), 5–16.CrossRefGoogle Scholar
[Cox]Coxeter, H. S. M.. Extreme forms. Canad. J. Math., 3 (1951). 391441.CrossRefGoogle Scholar
[PAR1]Cohen, H.Batut, C.Belabas, K.Bernardi, D. and Oliver, M.. User's Guide to PARI. http://www.parigp-home.deGoogle Scholar
[M]Martinet, J.. Perfect Lattices in Euclidean Spaces. Grundlehren 327, Springer-Verlag (Heidelberg, 2003).CrossRefGoogle Scholar
[M1]Martinet, J.. Sur l'indice d'un sous-réseau (with an appendix by C. Batut). In Reseaux Euclidiens, Designs Sphériques et Groupes (ed. Martinet, J.). L'Ens. Math.. Monographie 37, Genéve (2001), 163–211.Google Scholar
[M-V]Martinet, J. and Venkov, B.. On integral lattices having an odd minimum. J. Algebra and Analysis (Saint-Petersburg) 16, 3 (2004), 198–237.Google Scholar
[N-S]Nebe, G. and Sloane, N. J. A.. A Catalogue of Lattices, http://www.research.att.com~njas/lattices/index.htmlGoogle Scholar
[W]Watson, G. L.. On the minimum points of a positive quadratic form. Mathematika. 18 (1971), 60–70.CrossRefGoogle Scholar