{"paper":{"title":"Rich square-free words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.CO","authors_text":"Jetro Vesti","submitted_at":"2016-03-03T11:22:03Z","abstract_excerpt":"A word w is rich if it has |w|+1 many distinct palindromic factors, including the empty word. A word is square-free if it does not have a factor uu, where u is a non-empty word.\n  Pelantov\\'a and Starosta (Discrete Math. 313 (2013)) proved that every infinite rich word contains a square. We will give another proof for that result. Pelantov\\'a and Starosta denoted by r(n) the length of a longest rich square-free word on an alphabet of size n. The exact value of r(n) was left as an open question. We will give an upper and a lower bound for r(n), and make a conjecture that our lower bound is exac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01058","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"}