Transitive factorizations of free partially commutative monoids and Lie algebras
<|reference_start|>Transitive factorizations of free partially commutative monoids and Lie algebras: Let $\M(A,\theta)$ be a free partially commutative monoid. We give here a necessary and sufficient condition on a subalphabet $B\subset A$ such that the right factor of a bisection $\M(A,\theta)=\M(B,\theta\_B).T$ be also partially commutative free. This extends strictly the (classical) elimination theory on partial commutations and allows to construct new factorizations of $\M(A,\theta)$ and associated bases of $L\_K(A,\theta)$.<|reference_end|>
@article{luque2006transitive,
    title={Transitive factorizations of free partially commutative monoids and Lie
  algebras},
    author={Jean-Gabriel Luque (IGM-LabInfo), G'erard Henry Edmond Duchamp (LIPN)},
    journal={Discrete Mathematics 246, Issue 1-3 (2002) 83 - 97},
    year={2006},
    archivePrefix={arXiv},
    eprint={math/0607420},
    primaryClass={math.CO cs.DM cs.SC math.GM}
}