Let $W$ be a Coxeter group attached to a Coxeter matrix with entries $m_{ij}$ . The presentation of $W$ is given by $$W= < T_1, \dots, T_n | T_i^2=1, T_iT_jT_i \ldots = T_jT_iT_j \ldots, i \neq j>$$ where each side of the second equation has $m_{ij}$ terms.

Suppose $B_{W}$ is the corresponding braid group (aka Artin group) obtained by removing the relations $T_i^2=1$: $$B_{W}=< T_1, \dots, T_n | T_iT_jT_i \cdots = T_jT_iT_j \cdots>.$$

Then there is a canonical surjective homomorphism $B_{W} \to W$, the kernel of this homomorphism is called pure Artin group.

Does anyone know the presentation of the pure Artin group?

Thank you!