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Search: id:A090492
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| A090492 |
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G.f.: (1+x^10)/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)). |
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+0
2
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| 1, 0, 1, 1, 2, 2, 3, 3, 5, 5, 8, 7, 11, 11, 15, 16, 20, 21, 27, 28, 35, 36, 44, 46, 55, 58, 67, 71, 82, 86, 99, 103, 117, 123, 138, 145, 161, 169, 187, 196, 216, 225, 247, 258, 281, 294, 318, 332, 359, 374, 403, 419, 450, 468, 501, 521, 555, 577, 614, 637, 677, 701, 743, 770, 814
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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A_8 = SL_2(4) and acts on F_2[x_1, ..., x_4]. There are two copies of A_5 inside A_8. This is the Poincare series (or Molien series) for the subgroup A_5 acting on F_2[x_1, ..., x_4] by tensoring over F_2 from the action of S_5 on Z^4 where Z^4 consists of those elements (n_1, ..., n_5) with Sum n_i = 0. That is, A_5 acts on the sub-ring F_2[x_1 - x_5, x_2 - x_5, x_3 - x_5, x_4 - x_5] \subset F_2[x_1, \dots, x_5] by restriction to A_5 of the permutation S_5 action. See A089596 for the other A_5.
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REFERENCES
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A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 113.
H. Derksen and G. Kemper, Computational Invariant Theory, Springer, 2002; p. 130.
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LINKS
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Index entries for Molien series
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CROSSREFS
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Sequence in context: A026797 A027189 A116575 this_sequence A103609 A129526 A000358
Adjacent sequences: A090489 A090490 A090491 this_sequence A090493 A090494 A090495
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KEYWORD
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nonn
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AUTHOR
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njas, Feb 02 2004
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