{"paper":{"title":"Circular repetition thresholds on some small alphabets: Last cases of Gorbunova's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.CO","authors_text":"James D. Currie, Lucas Mol, Narad Rampersad","submitted_at":"2018-03-21T21:43:53Z","abstract_excerpt":"A word is called $\\beta$-free if it has no factors of exponent greater than or equal to $\\beta$. The repetition threshold $\\mathrm{RT}(k)$ is the infimum of the set of all $\\beta$ such that there are arbitrarily long $k$-ary $\\beta$-free words (or equivalently, there are $k$-ary $\\beta$-free words of every sufficiently large length, or even every length). These three equivalent definitions of the repetition threshold give rise to three natural definitions of a repetition threshold for circular words. The infimum of the set of all $\\beta$ such that\n  - there are arbitrarily long $k$-ary $\\beta$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08145","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"}