{"paper":{"title":"The maximal length of a gap between r-graph Tur\\'an densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Oleg Pikhurko","submitted_at":"2015-04-03T08:02:09Z","abstract_excerpt":"The Tur\\'an density $\\pi(\\cal F)$ of a family $\\cal F$ of $r$-graphs is the limit as $n\\to\\infty$ of the maximum edge density of an $\\cal F$-free $r$-graph on $n$ vertices. Erdos [Israel J. Math 2 (1964) 183--190] proved that no Tur\\'an density can lie in the open interval $(0,r!/r^r)$. Here we show that any other open subinterval of $[0,1]$ avoiding Tur\\'an densities has strictly smaller length. In particular, this implies a conjecture of Grosu [E-print arXiv:1403.4653v1, 2014]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00769","kind":"arxiv","version":1},"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"}