{"paper":{"title":"$\\omega$-Lyndon words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luca Q. Zamboni, Micka\\\"el Postic","submitted_at":"2019-07-01T20:56:16Z","abstract_excerpt":"Let $\\A$ be a finite non-empty set and $\\preceq $ a total order on $\\A^\\nats$ verifying the following lexicographic like condition: For each $n\\in \\nats$ and $u, v\\in \\A^n,$ if $u^\\omega \\prec v^\\omega$ then $ux\\prec vy$ for all $x, y \\in \\A^\\nats.$ A word $x\\in \\A^\\nats$ is called $\\omega$-Lyndon if $x\\prec y$ for each proper suffix $y$ of $x.$ A finite word $w\\in \\A^+$ is called $\\omega$-Lyndon if $w^\\omega \\prec v^\\omega$ for each proper suffix $v$ of $w.$ In this note we prove that every infinite word may be written uniquely as a non-increasing product of $\\omega$-Lyndon words."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01072","kind":"arxiv","version":2},"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"}