|
| |
|
|
A161409
|
|
Number of reduced words of length n in the Weyl group E_6 on 6 generators and order 51840.
|
|
120
|
|
|
|
1, 6, 20, 50, 105, 195, 329, 514, 754, 1048, 1389, 1765, 2159, 2549, 2911, 3222, 3461, 3611, 3662, 3611, 3461, 3222, 2911, 2549, 2159, 1765, 1389, 1048, 754, 514, 329, 195, 105, 50, 20, 6, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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.
|
|
|
LINKS
|
Table of n, a(n) for n=0..36.
Index entries for sequences related to groups
|
|
|
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
|
Cf. A161410, A154638.
Sequence in context: A162209 A161699 A216175 * A002415 A052515 A067117
Adjacent sequences: A161406 A161407 A161408 * A161410 A161411 A161412
|
|
|
KEYWORD
|
nonn,fini,full
|
|
|
AUTHOR
|
John Cannon and N. J. A. Sloane, Nov 29 2009
|
|
|
STATUS
|
approved
|
| |
|
|
