{"paper":{"title":"A characterization of connected self-affine fractals arising from collinear digits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Jun Jason Luo, King-Shun Leung","submitted_at":"2016-10-22T10:27:07Z","abstract_excerpt":"Let $A$ be an expanding integer matrix with characteristic polynomial $f(x)=x^{2}+px+q$, and let $\\mathcal{D}=\\{0,1,\\dots,|q|-2,|q|+m\\}\\mathbf{v}$ be a collinear digit set where $m\\geqslant 0, {\\mathbf v}\\in {\\mathbb Z}^2$. It is well known that there exists a unique self-affine fractal $T$ satisfying $AT=T+\\mathcal{D}$. In this paper, we give a complete characterization on the connected $T$. That generalizes the previous result of $|q|=3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07029","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"}