{"paper":{"title":"Algorithms to test open set condition for self-similar set related to P.V. numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Hao Li, Li-Feng Xi, Qin Wang, qiu-li Guo","submitted_at":"2014-05-05T05:22:37Z","abstract_excerpt":"Fix a P.V. number $\\lambda ^{-1}>1.$ Given $\\mathbf{p}=(p_{1},\\cdots,p_{m})\\in \\mathbb{N}^{m}$, $\\mathbf{b}=(b_{1},\\cdots,b_{m})\\in \\mathbb{Q^{m}$, for the self-similar set $E_{\\mathbf{p},\\mathbf{b}}=\\cup_{i=1}^{m}(\\lambda ^{p_{i}}E_{\\mathbf{p},\\mathbf{b}}+b_{i})$ we find an efficient algorithm to test whether $E_{\\mathbf{p},\\mathbf{b}}$ satisfies the open set condition (strong separation condition) or not."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0781","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"}