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A272696
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Coxeter number for the reflection group E_n.
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1
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OFFSET
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3,1
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COMMENTS
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A good definition of E_n is to take (-3,1,...,1)^perp in Z^(1,n) (and change the sign). This is the correct definition when one relates E_n to the blowup of P^2 at n points, and gives the sequence E_8, E_7, E_6, D_5, A_4, A_2 X A_1.
For n>8, the Coxeter number is infinity.
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REFERENCES
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J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.2, page 80.
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LINKS
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EXAMPLE
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Starting with the Coxeter-Dynkin diagram for E_8, one repeatedly chops off nodes from one end, getting the sequence E_8, E_7, E_6, D_5, A_4, A_2 X A_1, whose Coxeter numbers are 30, 18, 12, 8, 5, 3 X 2=6. - N. J. A. Sloane, May 05 2016
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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