{"paper":{"title":"Connectedness of self-affine sets with product digit sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GN","authors_text":"Jing-Cheng Liu, Jun Jason Luo, Ke Tang","submitted_at":"2016-03-19T12:14:42Z","abstract_excerpt":"Let $T(A,\\mathcal{D})$ be a self-affine set generated by an expanding matrix $A=\\left[\\begin{array}{rr} p & 0\\cr -a & q \\end{array}\\right]$ and a product digit set $\\mathcal{D}=\\{0,1,\\dots,m-1\\}\\times \\{0,1,\\dots,n-1\\}$. We provide a necessary and sufficient condition for the $T(A,\\mathcal{D})$ to be connected, which generalizes the known results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06087","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"}