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A161987

Number of reduced words of length n in the Weyl group B_32.
(history; published version)

#5 by Jon E. Schoenfield at Sun Jul 19 10:23:51 EDT 2015

STATUS

editing

approved

#4 by Jon E. Schoenfield at Sun Jul 19 10:23:50 EDT 2015

REFERENCES

J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincare Poincaré polynomial.

STATUS

approved

editing

#3 by N. J. A. Sloane at Sun Jul 13 09:05:25 EDT 2014

AUTHOR

_John Cannon (john(AT)maths.usyd.edu.au) _ and N. J. A. Sloane, Nov 30 2009

Discussion

Sun Jul 13

09:05

OEIS Server: https://oeis.org/edit/global/2246

#2 by Russ Cox at Fri Mar 30 16:51:25 EDT 2012

AUTHOR

John Cannon (john(AT)maths.usyd.edu.au) and _N. J. A. Sloane (njas(AT)research.att.com), _, Nov 30 2009

Discussion

Fri Mar 30

16:51

OEIS Server: https://oeis.org/edit/global/110

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Number of reduced words of length n in the Weyl group B_32.

DATA

1, 32, 527, 5952, 51831, 370976, 2271896, 12237280, 59146604, 260441632, 1057250877, 3994502272, 14156055636, 47361532160, 150411609649, 455543049760, 1321024921186, 3680779823776, 9884216117666, 25650056954016

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 Poincare polynomial.

N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)

FORMULA

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

KEYWORD

nonn

AUTHOR

John Cannon (john(AT)maths.usyd.edu.au) and N. J. A. Sloane (njas(AT)research.att.com), Nov 30 2009

STATUS

approved