{"paper":{"title":"Intersections of homogeneous Cantor sets and beta-expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Derong Kong, Michel Dekking, Wenxia Li","submitted_at":"2011-10-14T12:53:22Z","abstract_excerpt":"Let $\\Gamma_{\\beta,N}$ be the $N$-part homogeneous Cantor set with $\\beta\\in(1/(2N-1),1/N)$. Any string $(j_\\ell)_{\\ell=1}^\\N$ with $j_\\ell\\in\\{0,\\pm 1,...,\\pm(N-1)\\}$ such that $t=\\sum_{\\ell=1}^\\N j_\\ell\\beta^{\\ell-1}(1-\\beta)/(N-1)$ is called a code of $t$. Let $\\mathcal{U}_{\\beta,\\pm N}$ be the set of $t\\in[-1,1]$ having a unique code, and let $\\mathcal{S}_{\\beta,\\pm N}$ be the set of $t\\in\\mathcal{U}_{\\beta,\\pm N}$ which make the intersection $\\Gamma_{\\beta,N}\\cap(\\Gamma_{\\beta,N}+t)$ a self-similar set. We characterize the set $\\mathcal{U}_{\\beta,\\pm N}$ in a geometrical and algebraical w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3192","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"}