{"paper":{"title":"Repetition avoidance in products of factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Kamellia Reshadi, Pamela Fleischmann, Pascal Ochem","submitted_at":"2018-09-05T10:36:14Z","abstract_excerpt":"We consider a variation on a classical avoidance problem from combinatorics on words that has been introduced by Mousavi and Shallit at DLT 2013. Let $\\texttt{pexp}_i(w)$ be the supremum of the exponent over the products of $i$ factors of the word $w$. The repetition threshold $\\texttt{RT}_i(k)$ is then the infimum of $\\texttt{pexp}_i(w)$ over all words $w\\in\\Sigma^\\omega_k$. Mousavi and Shallit obtained that $\\texttt{RT}_i(2)=2i$ and $\\texttt{RT}_2(3)=\\tfrac{13}4$. We show that $\\texttt{RT}_i(3)=\\tfrac{3i}2+\\tfrac14$ if $i$ is even and $\\texttt{RT}_i(3)=\\tfrac{3i}2+\\tfrac16$ if $i$ is odd and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01426","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"}