{"paper":{"title":"Hausdorff dimension of unique beta expansions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Derong Kong, Wenxia Li","submitted_at":"2014-01-24T23:50:29Z","abstract_excerpt":"Given an integer $N\\ge 2$ and a real number ${\\beta}>1$, let $\\Gamma_{{\\beta},N}$ be the set of all $x=\\sum_{i=1}^\\infty {d_i}/{{\\beta}^i}$ with $d_i\\in\\{0,1,\\cdots,N-1\\}$ for all $i\\ge 1$. The infinite sequence $(d_i)$ is called a ${\\beta}$-expansion of $x$. Let $\\mathbf{U}_{{\\beta},N}$ be the set of all $x$'s in $\\Gamma_{{\\beta},N}$ which have unique ${\\beta}$-expansions. We give explicit formula of the Hausdorff dimension of $\\mathbf{U}_{{\\beta},N}$ for ${\\beta}$ in any admissible interval $[{{\\beta}}_L,{{\\beta}}_U]$, where ${{\\beta}_L}$ is a purely Parry number while ${{\\beta}_U}$ is a tra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6473","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"}