cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A272696 Coxeter number for the reflection group E_n.

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%I A272696 #31 Mar 13 2019 12:28:09
%S A272696 6,5,8,12,18,30
%N A272696 Coxeter number for the reflection group E_n.
%C A272696 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.
%C A272696 For n>8, the Coxeter number is infinity.
%D A272696 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.2, page 80.
%H A272696 Benedict H. Gross, Eriko Hironaka, and Curtis T. McMullen, <a href="https://doi.org/10.1016/j.jnt.2008.09.021">Cyclotomic factors of Coxeter polynomials</a>, Journal of Number Theory (2009) 129(5): 1034-1043. See <a href="http://nrs.harvard.edu/urn-3:HUL.InstRepos:3446011">also</a>.
%e A272696 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
%Y A272696 Cf. A272764.
%K A272696 nonn,fini,full
%O A272696 3,1
%A A272696 _Curtis T. McMullen_, May 04 2016