{"paper":{"title":"Regular Intersecting Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii, Ferdinand Ihringer","submitted_at":"2017-09-29T15:48:06Z","abstract_excerpt":"We call a family of sets intersecting, if any two sets in the family intersect. In this paper we investigate intersecting families $\\mathcal{F}$ of $k$-element subsets of $[n]:=\\{1,\\ldots, n\\},$ such that every element of $[n]$ lies in the same (or approximately the same) number of members of $\\mathcal{F}$. In particular, we show that we can guarantee $|\\mathcal{F}| = o({n-1\\choose k-1})$ if and only if $k=o(n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10462","kind":"arxiv","version":3},"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"}