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A091575 Poincaré series [or Poincare series] of the preprojective algebra of a Dynkin diagram of type E_8. 6
8, 14, 20, 26, 32, 38, 44, 48, 52, 56, 60, 62, 64, 64, 64, 64, 64, 62, 60, 56, 52, 48, 44, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

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

LINKS

Table of n, a(n) for n=0..82.

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A063288 A136798 A172182 * A091572 A096786 A114527

Adjacent sequences:  A091572 A091573 A091574 * A091576 A091577 A091578

KEYWORD

easy,nonn

AUTHOR

Paul Boddington, Jan 22 2004

STATUS

approved

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Last modified June 23 16:14 EDT 2021. Contains 345402 sequences. (Running on oeis4.)