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A033689 Number of extreme quadratic forms or lattices in dimension n. +0
2
1, 1, 1, 2, 3, 6, 30, 2408 (list; graph; listen)
OFFSET

1,4

REFERENCES

J. H. Conway and N. J. A. Sloane, Low-dimensional lattices III: perfect forms, Proc. Royal Soc. London, A 418 (1988), 43-80.

M. Dutour Sikiric, A. Schuermann and F. Vallentin, Classifiaction of eight-dimensional perfect forms, Preprint, 2006.

D.-O. Jaquet, Classification des reseaux dans R^7 (via la notion de formes parfaites), Journees Arithmetiques, 1989 (Luminy, 1989). Asterisque No. 198-200 (1991), 7-8, 177-185 (1992).

D.-O. Jaquet and F. Sigrist, Formes quadratiques contigues a D_7, C. R. Acad. Sci. Paris Ser. I Math. 309 (1989), no. 10, 641-644.

J. Martinet, Les reseaux parfaits des espaces Euclidiens, Masson, Paris, 1996, p. 175.

J. Martinet, Perfect Lattices in Euclidean Spaces, Springer-Verlag, NY, 2003.

G. Nebe, Review of J. Martinet, Perfect Lattices in Euclidean Spaces, Bull. Amer. Math. Soc., 41 (No. 4, 2004), 529-533.

C. Riener, On extreme forms in dimension 8, J. Theorie Nombres Bordeaux, to appear, 2006.

P. M. Gruber, Convex and Discrete Geometry, Springer, 2007; p. 439

LINKS

J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, 3rd edition, 1999, see Preface to 3rd Ed., especially the page that was omitted by the publisher between pages xx and xxi!

J. Martinet and B. Venkov, Les reseaux fortement eutactiques, pp. 112-132 in Reseaux Euclidiens, Designs Spheriques et Formes Modulaires, ed. J. Martinet, L'Enseignement Mathematiques, Geneva, 2001.

B. Venkov, Reseaux et designs spheriques, pp. 10-86 in Reseaux Euclidiens, Designs Spheriques et Formes Modulaires, ed. J. Martinet, L'Enseignement Mathematiques, Geneva, 2001.

CROSSREFS

Cf. A004026.

Sequence in context: A002234 A074005 A082611 this_sequence A018324 A129379 A000308

Adjacent sequences: A033686 A033687 A033688 this_sequence A033690 A033691 A033692

KEYWORD

nonn,nice,hard

AUTHOR

njas

EXTENSIONS

a(8) = 2408 was calculated by G. Nebe's student Cordian Riener - communicated by G. Nebe, Oct 11, 2005. He found this number by checking the complete list of 10916 perfect lattices in 8 dimensions (see A004026).

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Last modified July 6 17:22 EDT 2008. Contains 140988 sequences.


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