A065535 Number of strongly perfect lattices in dimension n.

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

Offset: 1

Author

N. J. A. Sloane, Nov 16 2001

Keywords

• nonn
• nice
• hard
• more

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

• 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.