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Search: id:A079293
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| A079293 |
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Degree of the numerator of Fn(z), the Poincare series (also Hilbert, Molien series) for C(Vn)^G where G=SL(2,C) and Vd is the space for binary forms of degree d. |
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1
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| 0, 0, 0, 18, 15, 48, 18, 66, 48, 102, 52, 146, 83, 192, 102, 252, 136, 320, 168, 396, 210, 480, 250, 572, 300, 672, 348, 780, 406, 896, 462, 1020, 528, 1152, 592, 1292, 666, 1440, 738
(list; graph; listen)
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OFFSET
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2,4
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COMMENT
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Fn(z) is a rational function of degree -(n+1). Recently Brouwer, Cohen and later Sally Jr. calculated Fn(z) for all n<=18 and n=20, 22, 24. It is rumored that Littelmann, Procesi, Laurent have calculated Fn(z) for many other values of n.
This sequence is somewhat badly defined. The values 18, 15, 48, 18 are not the degrees of the numerator of this rational function in lowest terms, but rather are degrees of a "representative" form. But there may be several representative forms with different degrees. [From Andries Brouwer (aeb(AT)cwi.nl), Jan 15 2009]
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REFERENCES
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Jean-Michel Kantor, Ou en sont les mathematiques?, SMF, Vuibert, Chapitre 5, paragraphe 6, "Invariants des formes binaires : la formule de Cayley-Sylvester", pp. 73-74
J. J. Sylvester, Proof of the hitherto undemonstrated fundamental theorem of invariants, Phil. Mag. 89,178-188,1878
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LINKS
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Andries Brouwer, Poincare Series
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EXAMPLE
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F8(z)=(1+z^8+z^9+z^10+z^18)/prod(i=2,7,1-z^i) hence a(8)=18
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CROSSREFS
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Sequence in context: A160901 A159502 A077668 this_sequence A070646 A094381 A074972
Adjacent sequences: A079290 A079291 A079292 this_sequence A079294 A079295 A079296
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KEYWORD
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more,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 08 2003
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