A104993 Molien series for a certain 16-dimensional group of order 20160.

1, 2, 4, 8, 16, 31, 61, 117, 224, 424, 796, 1476, 2717, 4938, 8876, 15756, 27616, 47764, 81542, 137356, 228363, 374755, 607213, 971675, 1536235, 2400465, 3708625, 5667325, 8569742, 12827751, 19015101, 27923781, 40638610, 58633470, 83896398, 119089492

Offset

0,2

Links

Table of n, a(n) for n=0..35.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Prog

(Magma) K:=Rationals(); M:=MatrixAlgebra(K, 4); q1:=DiagonalMatrix(M, [1, -1, 1, -1]); p1:=DiagonalMatrix(M, [1, 1, -1, -1]); q2:=DiagonalMatrix(M, [1, 1, 1, -1]); h:=M![1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1]/2; H:=MatrixGroup<4, K|q1, q2, h, p1>;
permstomats:=function(L); n:=#L[1]; M:=MatrixAlgebra(Rationals(), n); a:=#L; MM:=[]; for i in [1..a] do Append(~MM, M ! 0); end for; for i in [1..a] do for j in [1..n] do MM[i][j][L[i][j]]:=1; end for; end for; return MM; end function;
MM:=MatrixAlgebra(K, 16); hh:=TensorProduct(M ! 1, h); qq1:=TensorProduct(M ! 1, q1); pp1:=TensorProduct(M ! 1, p1); qq2:=TensorProduct(M ! 1, q2);
perm:=sub<Sym(16) | (3, 5)*(4, 6)*(11, 13)*(12, 14), (3, 7)*(4, 8)*(11, 15)*(12, 16), (2, 10)*(4, 12)*(6, 14)*(8, 16), (2, 9)*(4, 11)*(6, 13)*(8, 15)>; Order(perm);
pp:=Setseq(Generators(perm)); L:=[Eltseq(pp[1]), Eltseq(pp[2]), Eltseq(pp[3]), Eltseq(pp[4])]; ML:=permstomats(L); UU:=MatrixGroup<16, K | hh, qq2, ML[1], ML[2], ML[3], ML[4]>; Order(UU); MUU:=MolienSeries(UU);

Crossrefs

Sequence in context: A152718 A347776 A006775 * A223940 A189076 A192656

Adjacent sequences: A104990 A104991 A104992 * A104994 A104995 A104996

Keyword

nonn

Author

N. J. A. Sloane and Gabriele Nebe, Apr 26 2005

Status

approved