{"paper":{"title":"On prefixal factorizations of words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aldo de Luca, Luca Q. Zamboni","submitted_at":"2015-05-09T20:00:16Z","abstract_excerpt":"We consider the class ${\\cal P}_1$ of all infinite words $x\\in A^\\omega$ over a finite alphabet $A$ admitting a prefixal factorization, i.e., a factorization $x= U_0 U_1U_2 \\cdots $ where each $U_i$ is a non-empty prefix of $x.$ With each $x\\in {\\cal P}_1$ one naturally associates a \"derived\" infinite word $\\delta(x)$ which may or may not admit a prefixal factorization. We are interested in the class ${\\cal P}_{\\infty}$ of all words $x$ of ${\\cal P}_1$ such that $\\delta^n(x) \\in {\\cal P}_1$ for all $n\\geq 1$. Our primary motivation for studying the class ${\\cal P}_{\\infty}$ stems from its conn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02309","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"}