Solution
= Solution
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.