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A004027
Number of arithmetic n-dimensional crystal classes.
(Formerly M2060)
10
1, 2, 13, 73, 710, 6079, 85308
OFFSET
0,2
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
KEYWORD
nonn,hard,nice,more
EXTENSIONS
a(6) corrected from CARAT page by D. S. McNeil, Jan 02 2011
STATUS
approved