{"paper":{"title":"A square root map on Sturmian words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Jarkko Peltom\\\"aki, Markus Whiteland","submitted_at":"2015-09-21T19:16:45Z","abstract_excerpt":"We introduce a square root map on Sturmian words and study its properties. Given a Sturmian word of slope $\\alpha$, there exists exactly six minimal squares in its language (a minimal square does not have a square as a proper prefix). A Sturmian word $s$ of slope $\\alpha$ can be written as a product of these six minimal squares: $s = X_1^2 X_2^2 X_3^2 \\cdots$. The square root of $s$ is defined to be the word $\\sqrt{s} = X_1 X_2 X_3 \\cdots$. The main result of this paper is that that $\\sqrt{s}$ is also a Sturmian word of slope $\\alpha$. Further, we characterize the Sturmian fixed points of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06349","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":""},"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"}