# Signed symmetric group of finite degree is a Coxeter group

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Suppose $n$ is a nonnegative integer and $G$ is the signed symmetric group of degree $n + 1$. Then, $G$ is isomorphic to a Coxeter group with generators $s_1,s_2,\dots,s_n,t = s_{n+1}$, the $m_{ij}$ are as follows:
• $m_{i(i+1)} = 3$ for $1 \le i \le n - 1$
• $m_{n(n+1)} = 4$
• $m_{ij} = 2$ if $|i - j| > 1$
Under the isomorphism, $s_i$ is idnetified with the transposition $(i,i+1)$ and $t = s_{n+1}$ is the diagonal matrix with the last entry $-1$ and all remaining entries equal to $1$.