A004027 Number of arithmetic n-dimensional crystal classes.

1, 2, 13, 73, 710, 6079, 85308

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• nice
• more

Comments

Number of Z-classes of finite subgroups of GL_n(Z) up to conjugacy.

References

• H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space. Wiley, NY, 1978, p. 52.
• P. Engel, Geometric crystallography, in P. M. Gruber and J. M. Wills, editors, Handbook of Convex Geometry. North-Holland, Amsterdam, Vol. B, pp. 989-1041.
• R. L. E. Schwarzenberger, N-Dimensional Crystallography. Pitman, London, 1980, p. 34.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Akinari Hoshi, Ming-chang Kang and Aiichi Yamasaki, Multiplicative Invariant Fields of Dimension <= 6, Memoirs of the AMS, 2023.
• W. Plesken and T. Schulz, Dominik Bernhardt and others, Computer package CARAT
• W. Plesken and T. Schulz, CARAT Homepage [dead link]
• W. Plesken and T. Schulz, CARAT Homepage [Cached copy in pdf format (without subsidiary pages), with permission]
• W. Plesken and T. Schulz, Introduction to CARAT [Cached copy in pdf format (without subsidiary pages), with permission]
• W. Plesken and T. Schulz, Counting crystallographic groups in low dimensions, Experimental Mathematics, 9 (No. 3, 2000), 407-411.
• R. L. E. Schwarzenberger, Colour symmetry, Bulletin of the London Mathematical Society 16.3 (1984): 216-229.

Crossrefs

Cf. A004028, A004029, A006227, A307288.

Extensions

a(6) corrected from CARAT page by D. S. McNeil, Jan 02 2011