{"paper":{"title":"On the Convex Hulls of Self-Affine Fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ibrahim Kirat, Ilker Kocyigit","submitted_at":"2015-04-28T09:47:03Z","abstract_excerpt":"Suppose that the set ${\\mathcal{T}}= \\{T_1, T_2,...,T_q \\} $ of real $n\\times n$ matrices has joint spectral radius less than $1$. Then for any digit set $ D= \\{d_1, \\cdots, d_q\\} \\subset {\\Bbb R}^n$, there exists a unique nonempty compact set $F=F({\\mathcal{T}},D)$ satisfying $ F = \\bigcup _{j =1}^q T_j(F + d_j)$, which is called a self-affine fractal. We consider an existing criterion for the convex hull of $F$ to be a polytope, which is due to Kirat and Kocyigit. In this note, we strengthen our criterion for the case $T_1=T_2=\\cdots =T_q $. More specifically, we give an upper bound for the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07396","kind":"arxiv","version":3},"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"}