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A091575 Poincaré series [or Poincare series] of the preprojective algebra of a Dynkin diagram of type E_8. 6

%I

%S 8,14,20,26,32,38,44,48,52,56,60,62,64,64,64,64,64,62,60,56,52,48,44,

%T 38,32,26,20,14,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Poincaré series [or Poincare series] of the preprojective algebra of a Dynkin diagram of type E_8.

%D I. Reiten, Dynkin diagrams and the representation theory of algebras, Notices of the AMS, Vol. 44, Number 5.

%e The series is a polynomial because the algebra is finite dimensional. For an arbitrary Dynkin diagram the corresponding polynomial is (n+n*x^h-2*x^e_1-...-2*x^e_n)/(1-x)^2, where n is the rank, h the Coxeter number and e_1,...,e_n the Coxeter exponents of the associated Coxeter group.

%Y Cf. A089010, A091571, A091572, A091573, A091574, A091576, A091577.

%K easy,nonn

%O 0,1

%A _Paul Boddington_, Jan 22 2004

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Last modified July 24 06:56 EDT 2021. Contains 346273 sequences. (Running on oeis4.)