{"paper":{"title":"Improved bounds concerning the maximum degree of intersecting hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jian Wang, Peter Frankl","submitted_at":"2022-10-20T11:20:16Z","abstract_excerpt":"For positive integers $n>k>t$ let $\\binom{[n]}{k}$ denote the collection of all $k$-subsets of the standard $n$-element set $[n]=\\{1,\\ldots,n\\}$. Subsets of $\\binom{[n]}{k}$ are called $k$-graphs. A $k$-graph $\\mathcal{F}$ is called $t$-intersecting if $|F\\cap F'|\\geq t$ for all $F,F'\\in \\mathcal{F}$. One of the central results of extremal set theory is the Erd\\H{o}s-Ko-Rado Theorem which states that for $n\\geq (k-t+1)(t+1)$ no $t$-intersecting $k$-graph has more than $\\binom{n-t}{k-t}$ edges. For $n$ greater than this threshold the $t$-star (all $k$-sets containing a fixed $t$-set) is the onl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.11172","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.11172/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"}