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.

%I A293063 #12 Apr 09 2019 05:10:55
%S A293063 2,5,7,31,31,80,122,394,528,1651,1202
%N 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.
%C A293063 Magnetic groups are also known as antisymmetry groups, or black-white, or two-color crystallographic groups.
%C A293063 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 A293063 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 A293063 T(2,1) are band groups.
%C A293063 T(3,3) are Shubnikov groups.
%C A293063 For T(n,0) and T(n,n), see [Souvignier, 2006, table 1]. For rows 1-3, see Litvin.
%H A293063 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 A293063 D. B. Litvin, <a href="https://doi.org/10.1107/9780955360220001">Magnetic Group Tables</a>
%H A293063 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 A293063 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%e A293063 The triangle begins:
%e A293063      2;
%e A293063      5,   7;
%e A293063     31,  31,  80;
%e A293063    122, 394, 528, 1651;
%e A293063   1202, ...
%Y A293063 Cf. A293060, A293061, A293062, A307291.
%K A293063 nonn,tabl,hard,more
%O A293063 0,1
%A A293063 _Andrey Zabolotskiy_, Sep 29 2017