{"paper":{"title":"Toward the Combinatorial Limit Theory of Free Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Danny Rorabaugh","submitted_at":"2015-09-15T01:46:59Z","abstract_excerpt":"Free words are elements of a free monoid, generated over an alphabet via the binary operation of concatenation. Casually speaking, a free word is a finite string of letters. Henceforth, we simply refer to them as words. Motivated by recent advances in the combinatorial limit theory of graphs-notably those involving flag algebras, graph homomorphisms, and graphons-we investigate the extremal and asymptotic theory of pattern containment and avoidance in words. Word V is a factor of word W provided V occurs as consecutive letters within W. W is an instance of V provided there exists a nonerasing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04372","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"}