OFFSET
0,2
REFERENCES
N. Bourbaki, Groupes et algèbres de Lie, Chap. 4, 5, 6. (The group is defined in Planche V.)
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
FORMULA
G.f.: f(2)f(5)f(6)f(8)f(9)f(12)/f(1)^6 where f(k) = 1-x^k.
EXAMPLE
Coxeter matrix:
. [1 2 3 2 2 2]
. [2 1 2 3 2 2]
. [3 2 1 3 2 2]
. [2 3 3 1 3 2]
. [2 2 2 3 1 3]
. [2 2 2 2 3 1]
MATHEMATICA
CoefficientList[Series[((1-x^2) (1-x^5) (1-x^6) (1-x^8) (1-x^9) (1-x^12))/(1-x)^6, {x, 0, 40}], x] (* Harvey P. Dale, Aug 17 2011 *)
PROG
(Magma)
G := CoxeterGroup(GrpFPCox, "E6");
f := GrowthFunction(G);
Coefficients(PolynomialRing(IntegerRing())!f);
// Corrected by Klaus Brockhaus, Feb 12 2010
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
John Cannon and N. J. A. Sloane, Nov 29 2009
STATUS
approved