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 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 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

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Last modified March 31 05:57 EDT 2023. Contains 361634 sequences. (Running on oeis4.)