{"paper":{"title":"The Hypergraph Tur\\'{a}n Densities of Tight Cycles Minus an Edge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bernard Lidicky, Connor Mattes, Florian Pfender","submitted_at":"2024-09-21T22:46:43Z","abstract_excerpt":"A tight $\\ell$-cycle minus an edge $C_\\ell^-$ is the $3$-graph on the vertex set $[\\ell]$, where any three consecutive vertices in the string $123\\ldots\\ell 1$ form an edge. We show that for every $\\ell\\ge 5$, $\\ell$ not divisible by $3$, the extremal number is\n  $\n  ex\\left(C_\\ell^-,n\\right)=\\tfrac1{24}n^3+O(n\\ln n)=\\left(\\tfrac14+o(1)\\right){n\\choose 3}.\n  $\n  We determine the extremal graph up to $O(n)$ edge edits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.14257","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/2409.14257/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"}