{"paper":{"title":"Set Families with Low Pairwise Intersection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"Calvin Beideman, Jeremiah Blocki","submitted_at":"2014-04-17T19:38:20Z","abstract_excerpt":"A $\\left(n,\\ell,\\gamma\\right)$-sharing set family of size $m$ is a family of sets $S_1,\\ldots,S_m\\subseteq [n]$ s.t. each set has size $\\ell$ and each pair of sets shares at most $\\gamma$ elements. We let $m\\left(n,\\ell,\\gamma\\right)$ denote the maximum size of any such set family and we consider the following question: How large can $m\\left(n,\\ell,\\gamma\\right)$ be? $\\left(n,\\ell,\\gamma\\right)$-sharing set families have a rich set of applications including the construction of pseudorandom number generators and usable and secure password management schemes. We analyze the explicit construction"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4622","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"}