{"paper":{"title":"The independence number of non-uniform uncrowded hypergraphs and an anti-Ramsey type result","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hanno Lefmann, Sang June Lee","submitted_at":"2016-02-10T23:13:22Z","abstract_excerpt":"We prove the following: Fix an integer $k\\geq 2$, and let $T$ be a real number with $T\\geq 1.5$. Let $\\cH=(V,\\cE_2\\cup \\cE_3\\cup\\dots\\cup\\cE_k)$ be a non-uniform hypergraph with the vertex set $V$ and the set $\\cE_i$ of edges of size $i=2,\\ldots , k$. Suppose that $\\cH$ has no $2$-cycles (regardless of sizes of edges), and neither contains $3$-cycles nor $4$-cycles consisting of $2$-element edges. If the average degrees $t_i^{i-1} := i |\\cE_i|/ |V|$ satisfy that $t_i^{i-1} \\leq T^{i-1} (\\ln T)^{\\frac{k-i}{k-1}}$ for $i= 2, \\dots , k$, then there exists a constant $C_k > 0$, depending only on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03569","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"}