{"paper":{"title":"On the self similarity of generalized Cantor sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Derong Kong","submitted_at":"2012-07-16T12:32:50Z","abstract_excerpt":"We consider the self-similar structure of the class of generalized Cantor sets $$\\Gamma_{\\mathcal{D}}=\\Big\\{\\sum_{n=1}^\\infty d_n\\beta^{n}: d_n\\in D_n, n\\ge 1\\Big\\},$$ where $0<\\beta<1$ and $D_n, n\\ge 1,$ are nonempty and finite subsets of $\\mathbb{Z}$. We give a necessary and sufficient condition for $\\Gamma_{\\mathcal{D}}$ to be a homogeneously generated self similar set. An application to the self-similarity of intersections of generalized Cantor sets will be given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3652","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"}