A307291 -id:A307291 - cp's OEIS frontend

A293063 Triangle read by rows (n >= 0, 0 <= k <= n): T(n,k) = number of k-dimensional magnetic subperiodic groups in n-dimensional space, counting enantiomorphs.

2, 5, 7, 31, 31, 80, 122, 394, 528, 1651, 1202

Offset: 0

Andrey Zabolotskiy, Sep 29 2017

Magnetic groups are also known as antisymmetry groups, or black-white, or two-color crystallographic groups.
T(n,0) count n-dimensional magnetic crystallographic point groups, T(n,n) count n-dimensional magnetic space groups (A307291). The name "subperiodic groups" is usually related to the case 0 < k < n only, i.e., magnetic groups of n-dimensional objects including k independent translations which are subgroups of some n-dimensional magnetic space groups.
The Bohm-Koptsik symbols for these groups are G_{n,k}^1, except for the case k=n, when it is G_n^1.
T(2,1) are band groups.
T(3,3) are Shubnikov groups.
For T(n,0) and T(n,n), see [Souvignier, 2006, table 1]. For rows 1-3, see Litvin.

			The triangle begins:
     2;
     5,   7;
    31,  31,  80;
   122, 394, 528, 1651;
  1202, ...

H. Grimmer, Comments on tables of magnetic space groups, Acta Cryst., A65 (2009), 145-155.
D. B. Litvin, Magnetic Group Tables
B. Souvignier, The four-dimensional magnetic point and space groups, Z. Kristallogr., 221 (2006), 77-82.
Index entries for sequences related to groups

Cf. A293060, A293061, A293062, A307291.

A307290 Number of black-and-white colored (or proper magnetic) space groups in dimension n, counting enantiomorphs.

Original entry on oeis.org

0, 3, 46, 1191, 52439

Offset: 0

N. J. A. Sloane, Apr 08 2019

R. L. E. Schwarzenberger, Colour symmetry, Bulletin of the London Mathematical Society 16.3 (1984): 216-229.
B. Souvignier, Enantiomorphism of crystallographic groups in higher dimensions with results in dimensions up to 6, Acta Cryst., A59 (2003), 210-220.

Cf. A006227, A307291, A307292.

a(n) = A307291(n) - 2 * A006227(n). - Andrey Zabolotskiy, Apr 09 2019

a(0), a(4) from Andrey Zabolotskiy, Apr 09 2019

cp's OEIS Frontend

A293063 Triangle read by rows (n >= 0, 0 <= k <= n): T(n,k) = number of k-dimensional magnetic subperiodic groups in n-dimensional space, counting enantiomorphs.

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