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

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

Offset: 0

Author

Paul Boddington, Jan 22 2004

Keywords

• easy
• nonn

Examples

			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.
		

References

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

Crossrefs

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