{"paper":{"title":"Property O and Erd\\H{o}s--Szekeres properties in linear hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ander Lamaison, Minghui Ouyang, Suyun Jiang","submitted_at":"2025-09-10T15:33:22Z","abstract_excerpt":"An oriented $k$-uniform hypergraph, or oriented $k$-graph, is said to satisfy Property O if, for every linear ordering of its vertex set, there is some edge oriented consistently with this order. The minimum number $f(k)$ of edges in a $k$-graph with Property O was first studied by Duffus, Kay, and R\\\"{o}dl, and later improved by Kronenberg, Kusch, Lamaison, Micek, and Tran. In particular, they established the bounds $k! + 1 \\le f(k) \\le \\left(\\lfloor\\tfrac{k}{2}\\rfloor+1 \\right) k! - \\lfloor\\tfrac{k}{2}\\rfloor(k-1)!$ for every $k \\ge 2$.\n  In this note, we extend the study of Property O to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.08692","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.08692/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}