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Are the orders of the generators of a group and the product of pairs of thereof enough for this group to be isomorphic to a Coxeter group?
Let's say we have $n$ generators $x_1, x_2, \cdots, x_n$ along with the following facts concerning their orders:
\begin{eqnarray*}
ord(x_i) &=& 2 \text{ for } i = 1, 2, \cdots, n \\
ord(x_i ...
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