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Search: id:A091575
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| A091575 |
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Poincare series of the preprojective algebra of a Dynkin diagram of type E_8. |
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+0
7
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| 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; listen)
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OFFSET
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0,1
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REFERENCES
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I. Reiten, Dynkin diagrams and the representation theory of algebras, Notices of the AMS, Vol. 44, Number 5.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A089010, A091571, A091572, A091573, A091574, A091576, A091577.
Sequence in context: A125163 A063288 A136798 this_sequence A091572 A096786 A114527
Adjacent sequences: A091572 A091573 A091574 this_sequence A091576 A091577 A091578
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Boddington (psb(AT)maths.warwick.ac.uk), Jan 22 2004
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