The <Coxeter number> is the order of a <Coxeter element>. In the stated families the values are
$$
\begin{array}{c|c|c}
W&\text{Coxeter type}&h\\ \hline
D_{2n}&I_2(n)&n\\
S_n&A_{n-1}&n\\
SS_n&B_n&2n\\
ESS_n&D_n&2n-2.
\end{array}
$$
Here $D_{2n}$ is the <dihedral group> of order $2n$, $S_n$ is the <symmetric group>, $SS_n$ is the <signed symmetric group>, and $ESS_n$ is the <even signed symmetric group>.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 111 / 4 / a / Solution

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The Coxeter number is the <order of a group element>[order] of a <Coxeter element> in a finite irreducible <Coxeter group>.

Codex @codex  0

 Incoming links: Coxeter number