

A079293


Degree of the numerator of Fn(z), the Poincaré 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.


0



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;
refs;
listen;
history;
text;
internal format)



OFFSET

2,4


COMMENTS

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.  Andries E. Brouwer, Jan 15 2009


REFERENCES

JeanMichel Kantor, Où en sont les mathématiques?, SMF, Vuibert, Chapitre 5, paragraphe 6, "Invariants des formes binaires : la formule de CayleySylvester", pp. 7374.


LINKS

Table of n, a(n) for n=2..40.
Andries Brouwer, Poincaré Series.
A. E. Brouwer and A. M. Cohen, The Poincaré series of the polynomials invariant under SU2 in its irreducible representation of degree <=17, report ZW134, Math. Centr. Amsterdam, Dec. 1979.
J. J. Sylvester, Proof of the hitherto undemonstrated fundamental theorem of invariants, Phil. Mag. 30(5) (1878), 178188.
J. J. Sylvester, Proof of the hitherto undemonstrated fundamental theorem of invariants, Phil. Mag. 30(5) (1878), 178188.


EXAMPLE

F8(z) = (1 + z^8 + z^9 + z^10 + z^18)/Product_{i = 2..7} (1z^i), hence a(8) = 18.


CROSSREFS

Sequence in context: A077668 A298723 A299557 * A070646 A094381 A074972
Adjacent sequences: A079290 A079291 A079292 * A079294 A079295 A079296


KEYWORD

more,nonn


AUTHOR

Benoit Cloitre, Feb 08 2003


STATUS

approved



