{"paper":{"title":"Non-jumping Numbers for 5-Uniform Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kang Yang, Ran Gu, Xueliang Li, Yongtang Shi, Zhongmei Qin","submitted_at":"2013-12-12T03:35:32Z","abstract_excerpt":"Let $\\ell$ and $r$ be integers. A real number $\\alpha \\in [0,1)$ is a jump for $r$ if for any $\\varepsilon > 0$ and any integer $m,\\ m \\geq r$, any $r$-uniform graph with $n > n_0(\\varepsilon,m)$ vertices and at least \\alpha+ \\varepsilon)\\binom{n}{r}$ edges contains a subgraph with $m$ vertices and at least $(\\alpha +c)\\binom{m}{r}$ edges, where $c=c(\\alpha)$ does not depend on $\\varepsilon$ and $m$. It follows from a theorem of Erd\\H{o}s, Stone and Simonovits that every $\\alpha \\in [0,1)$ is a jump for $r=2$. Erd\\H{o}s asked whether the same is true for $r \\geq 3$. However, Frankl and R\\\"{o}d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3396","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":""},"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"}