{"paper":{"title":"Generalized Tur\\'an problem for Complete Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Levente Bodnar","submitted_at":"2023-02-15T10:27:56Z","abstract_excerpt":"Write $K^{(k)}_{n}$ for the complete $k$-graph on $n$ vertices. For $2 \\leq k \\leq g < r$ integers, let $\\pi\\left(n, K^{(k)}_{g}, K^{(k)}_r\\right)$ be the maximum density of $K^{(k)}_{g}$ in $n$ vertex $K^{(k)}_{r}$-free $k$-graphs. The main contribution of this paper is the upper bound: $\\pi\\left(n, K^{(k)}_{g}, K^{(k)}_r\\right) \\leq \\left(1 + O\\left(n^{-1}\\right) \\right)\\prod_{m=k}^{g} \\left(1 - \\frac{\\binom{m-1}{k-1}}{\\binom{r-1}{k-1}} \\right).$ The graph case ($k=2$) is the first known generalized Tur\\'an question, investigated by Erd\\H{o}s. The $k=g$ case is the hypergraph Tur\\'an problem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.07571","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/2302.07571/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"}