{"paper":{"title":"The Reversal Ratio of a Poset","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Graham Brightwell, Mitchel T. Keller","submitted_at":"2011-07-14T15:12:21Z","abstract_excerpt":"Felsner and Reuter introduced the linear extension diameter of a partially ordered set $\\mathbf{P}$, denoted $\\mbox{led}(\\mathbf{P})$, as the maximum distance between two linear extensions of $\\mathbf{P}$, where distance is defined to be the number of incomparable pairs appearing in opposite orders (reversed) in the linear extensions. In this paper, we introduce the reversal ratio $RR(\\mathbf{P})$ of $\\mathbf{P}$ as the ratio of the linear extension diameter to the number of (unordered) incomparable pairs. We use probabilistic techniques to provide a family of posets $\\mathbf{P}_k$ on at most "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2846","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"}