cp's OEIS Frontend

A293062 Triangle read by rows (n >= 0, 0 <= k <= n): T(n,k) = number of k-dimensional magnetic subperiodic groups in n-dimensional space, not counting enantiomorphs.

%I A293062 #8 Oct 07 2017 22:09:57
%S A293062 2,5,7,31,31,80,122,360,528,1594,1025
%N A293062 Triangle read by rows (n >= 0, 0 <= k <= n): T(n,k) = number of k-dimensional magnetic subperiodic groups in n-dimensional space, not counting enantiomorphs.
%C A293062 Magnetic groups are also known as antisymmetry groups, or black-white, or two-color crystallographic groups.
%C A293062 T(n,0) count n-dimensional magnetic crystallographic point groups, T(n,n) count n-dimensional magnetic space groups. 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 A293062 The Bohm-Koptsik symbols for these groups are G_{n,k}^1 (or G_{n+1,n,k}; the difference arises only when we consider enantiomorphism), except for the case k=n, when it is G_n^1 (or G_{n+1,n}).
%C A293062 T(2,1) are band groups.
%C A293062 T(3,3) are Shubnikov groups.
%C A293062 For T(n,0) and T(n,n), see [Souvignier, 2006, table 1]. See Litvin for the cases when there are no enantiomorphs: rows 1-2, T(3,2). For T(3,1), see, e.g., [Palistrant & Jablan, 1991].
%H A293062 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 A293062 D. B. Litvin, <a href="https://doi.org/10.1107/9780955360220001">Magnetic Group Tables</a>
%H A293062 A. F. Palistrant and S. V. Jablan, <a href="https://eudml.org/doc/255004">Enantiomorphism of three-dimensional space and line multiple antisymmetry groups</a>, Publications de l'Institut Mathématique, 49(63) (1991), 51-60.
%H A293062 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 A293062 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A293062 T(n,n) = A293060(n+1,n).
%e A293062 The triangle begins:
%e A293062      2;
%e A293062      5,   7;
%e A293062     31,  31,  80;
%e A293062    122, 360, 528, 1594;
%e A293062   1025, ...
%Y A293062 Cf. A293060, A293061, A293063.
%K A293062 nonn,tabl,hard,more
%O A293062 0,1
%A A293062 _Andrey Zabolotskiy_, Sep 29 2017