{"paper":{"title":"Transitive factorizations of free partially commutative monoids and Lie algebras","license":"","headline":"","cross_cats":["cs.DM","cs.SC","math.GM"],"primary_cat":"math.CO","authors_text":"G\\'erard Henry Edmond Duchamp (LIPN), Jean-Gabriel Luque (IGM-LabInfo)","submitted_at":"2006-07-18T12:42:33Z","abstract_excerpt":"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 $L\\_K(A,\\theta)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607420","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}