Talk:Coxeter–Dynkin diagram

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The content of the page is good. However the notation was (for me) rather non-standard.

In the book "Combinatorics of Coxeter groups" by Bjorner and Brenti (Springer texts in Mathematics) the irreducible Coxeter systems are given in Appendix A1. I believe their notations are much more standard in the literature. For the finite cases they use A_n, B_n, D_n for the families and E_6, E_7, E_8, F_4, G_2, H_3, H_4, I_2(m) for the others. The affine diagrams are \tilde{A}_1, \tilde{A}_{n-1}, \tilde{B}_n, \tilde{C}_n, \tilde{B}_n for the families and \tilde{E}_6, \tilde{E}_7, \tilde{E}_8, \tilde{F}_4, \tilde{G}_2 for the exceptional cases.

I think that using a standard notation, or at the very least making references to standard textbooks, would improve the page considerably.

Best regards, 140.105.47.81 10:08, 22 May 2007 (UTC)

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[edit] Graphics element documentation

Coxeter-Dynkins graphics on Wikipedia:

These component elements can be strung together to create linear diagrams. They are 23 pixels tall. The elements are variable width, (making them hard to systematically scale with "px" pixel-width codes). This set allows two sorts of nonlinear graphs, a central linear one that can branch up and down, and two rows top/bottom (a and b), that can be vertically connected and looped. They are largely complete for the finite and affine groups, but the triangle groups can't be labeled in general.

The small dots represent the graph nodes of a Coxeter group, while the ringed (circled) and ringed (hollow) nodes are used in the generation of Coxeter-Dynkin diagrams representing the uniform polytopes of Coxeter.