A162493 - OEIS

%I #10 Sep 08 2022 08:45:46

%S 1,7,27,77,182,378,713,1247,2051,3205,4795,6909,9632,13040,17194,

%T 22134,27874,34398,41657,49567,58009,66831,75852,84868,93659,101997,

%U 109655,116417,122087,126497,129514,131046,131046,129514,126497,122087,116417,109655

%N Number of reduced words of length n in the Weyl group E_7 on 7 generators and order 2903040.

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

%D H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, Table 10.

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

%H Jinyuan Wang, <a href="/A162493/b162493.txt">Table of n, a(n) for n = 0..63</a>

%F G.f.: (1-x^2)*(1-x^6)*(1-x^8)*(1-x^10)*(1-x^12)*(1-x^14)*(1-x^18)/(1-x)^7.

%o (Magma) G := CoxeterGroup(GrpFPCox, "E7");

%o f := GrowthFunction(G);

%o Coefficients(f);

%o (PARI) Vec((1-x^2)*(1-x^6)*(1-x^8)*(1-x^10)*(1-x^12)*(1-x^14)*(1-x^18)/(1-x)^7 + O(x^64)) \\ _Jinyuan Wang_, Mar 08 2020

%Y Cf. A161409, A162494.

%K nonn,fini,full

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 01 2009