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%I #12 Apr 09 2019 05:10:55
%S 2,5,7,31,31,80,122,394,528,1651,1202
%N 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.
%C Magnetic groups are also known as antisymmetry groups, or black-white, or two-color crystallographic groups.
%C 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.
%C The Bohm-Koptsik symbols for these groups are G_{n,k}^1, except for the case k=n, when it is G_n^1.
%C T(2,1) are band groups.
%C T(3,3) are Shubnikov groups.
%C For T(n,0) and T(n,n), see [Souvignier, 2006, table 1]. For rows 1-3, see Litvin.
%H H. Grimmer, <a href="https://doi.org/10.1107/S0108767308039007">Comments on tables of magnetic space groups</a>, Acta Cryst., A65 (2009), 145-155.
%H D. B. Litvin, <a href="https://doi.org/10.1107/9780955360220001">Magnetic Group Tables</a>
%H B. Souvignier, <a href="https://doi.org/10.1524/zkri.2006.221.1.77">The four-dimensional magnetic point and space groups</a>, Z. Kristallogr., 221 (2006), 77-82.
%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%e The triangle begins:
%e 2;
%e 5, 7;
%e 31, 31, 80;
%e 122, 394, 528, 1651;
%e 1202, ...
%Y Cf. A293060, A293061, A293062, A307291.
%K nonn,tabl,hard,more
%O 0,1
%A _Andrey Zabolotskiy_, Sep 29 2017
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