{"paper":{"title":"Levelness of toric rings arising from order and chain polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani, Takayuki Hibi","submitted_at":"2018-09-22T18:03:40Z","abstract_excerpt":"Let $K[\\mathcal{O}(P)]$ denote the toric ring of the order polytope $\\mathcal{O}(P)$ of a finite partially ordered set $P$ and $K[\\mathcal{C}(P)]$ that of the chain polytope $\\mathcal{C}(P)$. It will be shown that $\\beta_{p, p+j}(K[\\mathcal{O}(P)]) = \\beta_{p, p+j}(K[\\mathcal{C}(P)])$ for all $j \\geq 0$, where $p$ is the projective dimension of $K[\\mathcal{O}(P)]$ (and that of $K[\\mathcal{C}(P)]$). In particular, $K[\\mathcal{O}(P)]$ is level if and only if $K[\\mathcal{C}(P)]$ is level."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08462","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"}