{"paper":{"title":"Counting intersecting and pairs of cross-intersecting families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii, Peter Frankl","submitted_at":"2017-01-15T21:01:55Z","abstract_excerpt":"A family of subsets of $\\{1,\\ldots,n\\}$ is called {\\it intersecting} if any two of its sets intersect. A classical result in extremal combinatorics due to Erd\\H{o}s, Ko, and Rado determines the maximum size of an intersecting family of $k$-subsets of $\\{1,\\ldots, n\\}$. In this paper we study the following problem: how many intersecting families of $k$-subsets of $\\{1,\\ldots, n\\}$ are there? Improving a result of Balogh, Das, Delcourt, Liu, and Sharifzadeh, we determine this quantity asymptotically for $n\\ge 2k+2+2\\sqrt{k\\log k}$ and $k\\to \\infty$. Moreover, under the same assumptions we also d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04110","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"}