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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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+0
1
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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.
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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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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: A040308 A077810 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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