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A033689 Number of extreme quadratic forms or lattices in dimension n. 1
1, 1, 1, 2, 3, 6, 30, 2408 (list; graph; refs; listen; history; text; internal format)
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, Classification of eight-dimensional perfect forms, Preprint, 2006.

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

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.

A. Schuermann, Enumerating perfect forms, Contemporary Math., 493 (2009), 359-377. [From N. J. A. Sloane, Jan 21 2010]

LINKS

Table of n, a(n) for n=1..8.

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.

C. Riener, On extreme forms in dimension 8, J. Théor. Nombres Bordeaux 18 (2006), no. 3, 677-682.

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: A145499 A221310 A082611 * A018324 A178175 A129379

Adjacent sequences:  A033686 A033687 A033688 * A033690 A033691 A033692

KEYWORD

nonn,nice,hard

AUTHOR

N. J. A. Sloane.

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).

STATUS

approved

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Last modified October 22 19:18 EDT 2014. Contains 248400 sequences.