|
|
A162376
|
|
Number of reduced words of length n in the Weyl group D_29.
|
|
49
|
|
|
1, 29, 434, 4466, 35524, 232812, 1308509, 6482689, 28879476, 117441764, 441128513, 1544927933, 5083859819, 15819621191, 46800677805, 132236761657, 358269068693, 933922599849, 2349408360136, 5718723151160, 13500485623812
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
REFERENCES
|
N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche IV.)
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
|
|
LINKS
|
|
|
FORMULA
|
The growth series for D_k is the polynomial f(k)*Product_{i=1..k-1} f(2*i), where f(m) = (1-x^m)/(1-x) [Corrected by N. J. A. Sloane, Aug 07 2021]. This is a row of the triangle in A162206.
|
|
MAPLE
|
# Growth series for D_k, truncated to terms of order M. - N. J. A. Sloane, Aug 07 2021
f := proc(m::integer) (1-x^m)/(1-x) ; end proc:
g := proc(k, M) local a, i; global f;
a:=f(k)*mul(f(2*i), i=1..k-1);
seriestolist(series(a, x, M+1));
end proc;
|
|
MATHEMATICA
|
f[m_] := (1-x^m)/(1-x);
With[{k = 29}, CoefficientList[f[k]*Product[f[2i], {i, 1, k-1}] + O[x]^(k-8), x]] (* Jean-François Alcover, Feb 15 2023, after Maple code *)
|
|
CROSSREFS
|
Growth series for groups D_n, n = 3,...,50: A161435, A162207, A162208, A162209, A162210, A162211, A162212, A162248, A162288, A162297, A162300, A162301, A162321, A162327, A162328, A162346, A162347, A162359, A162360, A162364, A162365, A162366, A162367, A162368, A162369, A162370, A162376, A162377, A162378, A162379, A162380, A162381, A162384, A162388, A162389, A162392, A162399, A162402, A162403, A162411, A162412, A162413, A162418, A162452, A162456, A162461, A162469, A162492; also A162206.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|