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A162494
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Number of reduced words of length n in the Weyl group E_8 on 8 generators and order 696729600.
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4
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1, 8, 35, 112, 294, 672, 1386, 2640, 4718, 8000, 12978, 20272, 30645, 45016, 64470, 90264, 123829, 166768, 220849, 287992, 370250, 469784, 588833, 729680, 894613, 1085880, 1305640, 1555912, 1838523, 2155056, 2506798, 2894688, 3319268, 3780640, 4278429
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OFFSET
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0,2
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REFERENCES
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N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche VII.)
H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, Table 10.
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
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LINKS
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FORMULA
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G.f.: (1-x^2)*(1-x^8)*(1-x^12)*(1-x^14)*(1-x^18)*(1-x^20)*(1-x^24)*(1-x^30)/(1-x)^8.
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MATHEMATICA
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CoefficientList[Series[(1 - x^2) (1 - x^8) (1 - x^12) (1 - x^14) (1 - x^18) (1 - x^20) (1 - x^24) (1 - x^30) / (1 - x)^8, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 09 2013 *)
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PROG
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(Magma) G := CoxeterGroup(GrpFPCox, "E8");
f := GrowthFunction(G);
Coefficients(f);
(PARI) Vec((1-x^2)*(1-x^8)*(1-x^12)*(1-x^14)*(1-x^18)*(1-x^20)*(1-x^24)*(1-x^30)/(1-x)^8 + O(x^121)) \\ Jinyuan Wang, Mar 08 2020
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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