Coxeter Element
For a Coxeter group with simple generators s_1, ..., s_n, a Coxeter element is a product of the simple generators in some order, such as s_1...s_n. In a finite irreducible Coxeter group (one whose Coxeter-Dynkin diagram is connected), all Coxeter elements are conjugate and have the same order, called the Coxeter number.
See also
Coxeter-Dynkin Diagram, Coxeter Group, Coxeter Number, Coxeter PlaneExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
Humphreys, J. E. Reflection Groups and Coxeter Groups. Cambridge, England: Cambridge University Press, 1990.Cite this as:
Weisstein, Eric W. "Coxeter Element." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CoxeterElement.html