A065535 Number of strongly perfect lattices in dimension n.

1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0

Offset

1,1

Comments

It is known that a(12) through a(24) are at least 1, 0, 1, 0, 3, 0, 1, 0, 1, 1, 5, 4, 2 respectively.

In this sequence, the dual pairs of lattices are counted as one if they are both strongly perfect (it is not always so). E.g., in dimensions 6, 7, 10 there are two strongly perfect lattices, forming a dual pair, but in dimension 21 there is a strongly perfect lattice which has a not strongly perfect dual. - Andrey Zabolotskiy, Feb 20 2021

References

J. Martinet, Les réseaux parfaits des espaces euclidiens, Masson, Paris, 1996.

J. Martinet, Perfect Lattices in Euclidean Spaces, Springer-Verlag, NY, 2003. See Section 16.2.

Links

Table of n, a(n) for n=1..11.

B. Venkov, Réseaux et designs sphériques, pp. 10-86 in Réseaux Euclidiens, Designs Sphériques et Formes Modulaires, ed. J. Martinet, L'Enseignement Mathématique, Geneva, 2001.

Jacques Martinet, Known strongly perfect lattices, 2002-2020.

Crossrefs

Cf. A037075, A065536, A004026.

Sequence in context: A371691 A103842 A286064 * A285518 A093719 A153778

Adjacent sequences: A065532 A065533 A065534 * A065536 A065537 A065538

Keyword

nonn,nice,hard,more

Author

N. J. A. Sloane, Nov 16 2001

Status

approved