{"paper":{"title":"Order-Chain Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akiyoshi Tsuchiya, Lili Mu, Nan Li, Takayuki Hibi, Teresa Xueshan Li","submitted_at":"2015-04-07T19:08:39Z","abstract_excerpt":"Given two families $X$ and $Y$ of integral polytopes with nice combinatorial and algebraic properties, a natural way to generate new class of polytopes is to take the intersection $\\mathcal{P}=\\mathcal{P}_1\\cap\\mathcal{P}_2$, where $\\mathcal{P}_1\\in X$, $\\mathcal{P}_2\\in Y$. Two basic questions then arise: 1) when $\\mathcal{P}$ is integral and 2) whether $\\mathcal{P}$ inherits the \"old type\" from $\\mathcal{P}_1, \\mathcal{P}_2$ or has a \"new type\", that is, whether $\\mathcal{P}$ is unimodularly equivalent to some polytope in $X\\cup Y$ or not. In this paper, we focus on the families of order pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01706","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"}