{"paper":{"title":"Intersecting families of discrete structures are typically trivial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hong Liu, J\\'ozsef Balogh, Maryam Sharifzadeh, Michelle Delcourt, Shagnik Das","submitted_at":"2014-08-11T21:15:59Z","abstract_excerpt":"The study of intersecting structures is central to extremal combinatorics. A family of permutations $\\mathcal{F} \\subset S_n$ is \\emph{$t$-intersecting} if any two permutations in $\\mathcal{F}$ agree on some $t$ indices, and is \\emph{trivial} if all permutations in $\\mathcal{F}$ agree on the same $t$ indices. A $k$-uniform hypergraph is \\emph{$t$-intersecting} if any two of its edges have $t$ vertices in common, and \\emph{trivial} if all its edges share the same $t$ vertices.\n  The fundamental problem is to determine how large an intersecting family can be. Ellis, Friedgut and Pilpel proved th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2559","kind":"arxiv","version":4},"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"}