A161457 Number of reduced words of length n in the Weyl group A_9.

1, 9, 44, 155, 440, 1068, 2298, 4489, 8095, 13640, 21670, 32683, 47043, 64889, 86054, 110010, 135853, 162337, 187959, 211089, 230131, 243694, 250749, 250749, 243694, 230131, 211089, 187959, 162337, 135853, 110010, 86054, 64889, 47043, 32683, 21670, 13640, 8095, 4489, 2298, 1068, 440, 155, 44, 9, 1

Offset: 0

Author

John Cannon and N. J. A. Sloane, Nov 30 2009

Keywords

• fini
• nonn
• full

Comments

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

References

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

Crossrefs

Cf. A008302, A161409.

Programs

Mathematica

CoefficientList[Series[QFactorial[9+1,q],{q,0,9*(9+1)/2}],q] (* Wouter Meeussen, Jul 12 2014 *)

Formula

G.f. for A_m is the polynomial Product_{k=1..m} (1-x^(k+1))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A008302.