{"paper":{"title":"Convex Set of Doubly Substochastic Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lei Deng, Qiulin Lin","submitted_at":"2017-11-18T06:27:24Z","abstract_excerpt":"Denote $\\mathcal{A}$ as the set of all doubly substochastic $m \\times n$ matrices and let $k$ be a positive integer. Let $\\mathcal{A}_k$ be the set of all $1/k$-bounded doubly substochastic $m \\times n$ matrices, i.e., $\\mathcal{A}_k \\triangleq \\{E \\in \\mathcal{A}: e_{i,j} \\in [0, 1/k], \\forall i=1,2,\\cdots,m, j = 1,2,\\cdots, n\\}$. Denote $\\mathcal{B}_k$ as the set of all matrices in $\\mathcal{A}_k$ whose entries are either $0$ or $1/k$. We prove that $\\mathcal{A}_k$ is the convex hull of all matrices in $\\mathcal{B}_k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06818","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"}