{"paper":{"title":"The undirected repetition threshold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.FL"],"primary_cat":"math.CO","authors_text":"James D. Currie, Lucas Mol","submitted_at":"2019-04-22T18:53:14Z","abstract_excerpt":"For rational $1<r\\leq 2$, an undirected $r$-power is a word of the form $xyx'$, where $x$ is nonempty, $x'\\in\\{x,x^\\mathrm{R}\\}$, and $|xyx'|/|xy|=r$. The undirected repetition threshold for $k$ letters, denoted $\\mathrm{URT}(k)$, is the infimum of the set of all $r$ such that undirected $r$-powers are avoidable on $k$ letters. We first demonstrate that $\\mathrm{URT}(3)=\\tfrac{7}{4}$. Then we show that $\\mathrm{URT}(k)\\geq \\tfrac{k-1}{k-2}$ for all $k\\geq 4$. We conjecture that $\\mathrm{URT}(k)=\\tfrac{k-1}{k-2}$ for all $k\\geq 4$, and we confirm this conjecture for $k\\in\\{4,8,12\\}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10029","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"}