{"paper":{"title":"Fractional cross intersecting families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ritabrata Ray, Rogers Mathew, Shashank Srivastava","submitted_at":"2019-03-05T14:55:48Z","abstract_excerpt":"Let $\\mathcal{A}=\\{A_{1},...,A_{p}\\}$ and $\\mathcal{B}=\\{B_{1},...,B_{q}\\}$ be two families of subsets of $[n]$ such that for every $i\\in [p]$ and $j\\in [q]$, $|A_{i}\\cap B_{j}|= \\frac{c}{d}|B_{j}|$, where $\\frac{c}{d}\\in [0,1]$ is an irreducible fraction. We call such families \"$\\frac{c}{d}$-cross intersecting families\". In this paper, we find a tight upper bound for the product $|\\mathcal{A}||\\mathcal{B}|$ and characterize the cases when this bound is achieved for $\\frac{c}{d}=\\frac{1}{2}$. Also, we find a tight upper bound on $|\\mathcal{A}||\\mathcal{B}|$ when $\\mathcal{B}$ is $k$-uniform an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01872","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":""},"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"}