{"paper":{"title":"Conjugates of characteristic Sturmian words generated by morphisms","license":"","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Amy Glen","submitted_at":"2007-08-31T16:26:57Z","abstract_excerpt":"This article is concerned with characteristic Sturmian words of slope $\\alpha$ and $1-\\alpha$ (denoted by $c_\\alpha$ and $c_{1-\\alpha}$ respectively), where $\\alpha \\in (0,1)$ is an irrational number such that $\\alpha = [0;1+d_1,\\bar{d_2,...,d_n}]$ with $d_n \\geq d_1 \\geq 1$. It is known that both $c_\\alpha$ and $c_{1-\\alpha}$ are fixed points of non-trivial (standard) morphisms $\\sigma$ and $\\hat{\\sigma}$, respectively, if and only if $\\alpha$ has a continued fraction expansion as above. Accordingly, such words $c_\\alpha$ and $c_{1-\\alpha}$ are generated by the respective morphisms $\\sigma$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.4387","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0708.4387/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"}