{"paper":{"title":"Univoque numbers and an avatar of Thue-Morse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Christiane Frougny, Jean-Paul Allouche","submitted_at":"2007-12-01T19:14:22Z","abstract_excerpt":"Univoque numbers are real numbers $\\lambda > 1$ such that the number 1 admits a unique expansion in base $\\lambda$, i.e., a unique expansion $1 = \\sum_{j \\geq 0} a_j \\lambda^{-(j+1)}$, with $a_j \\in \\{0, 1, ..., \\lceil \\lambda \\rceil -1\\}$ for every $j \\geq 0$. A variation of this definition was studied in 2002 by Komornik and Loreti, together with sequences called {\\em admissible sequences}. We show how a 1983 study of the first author gives both a result of Komornik and Loreti on the smallest admissible sequence on the set $\\{0, 1, >..., b\\}$, and a result of de Vries and Komornik (2007) on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.0102","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"}