A351831 Vector in the 26-dimensional even Lorentzian unimodular lattice II_25,1 used to construct the Leech lattice.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 70

Offset: 1

Author

Paolo Xausa, Feb 21 2022

Keywords

• nonn
• easy
• fini
• full

Comments

As noted by Conway and Sloane (1999), the only nontrivial solution of 0^2 + 1^2 + ... + m^2 = n^2 in positive integers is m = 24, n = 70, allowing them to use the vector (0, 1, 2, 3, ..., 23, 24 | 70) to construct the Leech lattice.

Links

• Richard E. Borcherds, How to construct the Leech lattice, YouTube video, 2022.
• J. H. Conway and N. J. A. Sloane, Lorentzian forms for the Leech lattice, Bulletin (New Series) of the American Mathematical Society, Volume 6, Number 2, March 1982.
• J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 3rd edition, Springer, New York, NY, 1999, pp. 524-528.
• Wikipedia, II_25,1.
• Wikipedia, Leech lattice.

Crossrefs

Cf. A008408, A260646, A351830.

Programs

Mathematica

Append[Range[0,24],70]