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A104993 Molien series for a certain 16-dimensional group of order 20160. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A239556 A152718 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

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Last modified September 24 14:00 EDT 2020. Contains 337321 sequences. (Running on oeis4.)