{"paper":{"title":"The numbers of edges of the order polytope and the chain poyltope of a finite partially ordered set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Shikama, Nan Li, Takayuki Hibi, Yoshimi Sahara","submitted_at":"2015-08-02T04:15:31Z","abstract_excerpt":"Let $P$ be an arbitrary finite partially ordered set. It will be proved that the number of edges of the order polytope ${\\mathcal O}(P)$ is equal to that of the chain polytope ${\\mathcal C}(P)$. Furthermore, it will be shown that the degree sequence of the finite simple graph which is the $1$-skeleton of ${\\mathcal O}(P)$ is equal to that of ${\\mathcal C}(P)$ if and only if ${\\mathcal O}(P)$ and ${\\mathcal C}(P)$ are unimodularly equivalent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00187","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"}