{"paper":{"title":"Maximum Rectilinear Crossing Number of Uniform Hypergraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ayan, Rahul Gangopadhyay","submitted_at":"2019-08-13T14:18:24Z","abstract_excerpt":"We improve the lower bound on the $d$-dimensional rectilinear crossing number of the complete $d$-uniform hypergraph having $2d$ vertices to $\\Omega\\left(\\dfrac{(4\\sqrt{2}/3^{3/4})^d}{d}\\right)$ from $\\Omega(2^d \\sqrt{d})$. We also establish that the $3$-dimensional rectilinear crossing number of a complete $3$-uniform hypergraph having $n \\geq 9$ vertices is at least $\\dfrac{43}{42}\\dbinom{n}{6}$.\n  We prove that the maximum number of crossing pairs of hyperedges in a $4$-dimensional rectilinear drawing of the complete $4$-uniform hypergraph having $n$ vertices is $13\\dbinom{n}{8}$. We also p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04654","kind":"arxiv","version":6},"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/1908.04654/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"}