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A004026 Number of perfect quadratic forms or lattices in dimension n.
(Formerly M0862)
+0
7
1, 1, 1, 2, 3, 7, 33, 10916 (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.

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!

Mathieu Dutour Sikiric, Achill Schuermann and Frank Vallentin, Complete list of perfect forms in dimension 8

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. A033689, A065535, A065536, A037075, A122079, A122080.

Adjacent sequences: A004023 A004024 A004025 this_sequence A004027 A004028 A004029

Sequence in context: A057677 A032148 A101484 this_sequence A135907 A034900 A079388

KEYWORD

hard,nonn,nice

AUTHOR

njas

EXTENSIONS

a(8) from the work of Mathieu Dutour Sikiric, Achill Schuermann and Frank Vallentin, Oct 05 2005.

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Last modified May 16 01:24 EDT 2008. Contains 139630 sequences.


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