{"paper":{"title":"Functions on Antipower Prefix Lengths of the Thue-Morse Word","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shyam Narayanan","submitted_at":"2017-05-17T18:49:21Z","abstract_excerpt":"We say that a word $w$ of length $kn$ is a $k$-\\textit{antipower} if it can be written in the form $w_1 \\cdots w_k$, where each $w_i$ is a distinct word of length $n$. We analyze prefixes of the Thue-Morse word $\\textbf{t}$ and lengths of antipowers occurring in them. Define $\\Gamma(k)$ to be the largest odd $n$ such that the prefix of $\\textbf{t}$ of length $kn$ is not a $k$-antipower, and $\\gamma(k)$ to be the smallest odd $n$ such that the corresponding prefix is a $k$-antipower. We provide strong bounds on the asymptotic values of $\\gamma(k)$ and $\\Gamma(k)-\\gamma(k)$. Our bounds on $\\gamm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06310","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1705.06310/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}