

A161698


Number of reduced words of length n in the Weyl group B_5.


0



1, 5, 14, 30, 54, 86, 125, 169, 215, 259, 297, 325, 340, 340, 325, 297, 259, 215, 169, 125, 86, 54, 30, 14, 5, 1
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OFFSET

0,2


COMMENTS

Computed with MAGMA using commands similar to those used to compute A161409.


REFERENCES

J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
N. Bourbaki, Groupes et algèbres. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)


LINKS



FORMULA

G.f. for B_m is the polynomial Prod_{k=1..m}(1x^(2k))/(1x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.


MAPLE

seq(coeff(series(mul((1x^(2*k))/(1x), k=1..5), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 25 2018


MATHEMATICA

CoefficientList[Series[Product[(1x^(2*k)), {k, 1, 5}] /(1x)^5, {x, 0, 25}], x] (* G. C. Greubel, Oct 25 2018 *)


PROG

(PARI) t='t+O('t^26); Vec(prod(k=1, 5, 1t^(2*k))/(1t)^5) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=26; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1t^(2*k): k in [1..5]])/(1t)^5)); // G. C. Greubel, Oct 25 2018


CROSSREFS



KEYWORD

nonn,fini,full


AUTHOR



STATUS

approved



