{"paper":{"title":"On the complexity function for sequences which are not uniformly recurrent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nic Ormes, Ronnie Pavlov","submitted_at":"2019-07-15T17:57:31Z","abstract_excerpt":"We prove that every non-minimal transitive subshift $X$ satisfying a mild aperiodicity condition satisfies $\\limsup c_n(X) - 1.5n = \\infty$, and give a class of examples which shows that the threshold of $1.5n$ cannot be increased. As a corollary, we show that any transitive $X$ satisfying $\\limsup c_n(X) - n = \\infty$ and $\\limsup c_n(X) - 1.5n < \\infty$ must be minimal. We also prove some restrictions on the structure of transitive non-minimal $X$ satisfying $\\liminf c_n(X) - 2n = -\\infty$, which imply unique ergodicity (for a periodic measure) as a corollary, which extends a result of Boshe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06626","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"}