{"paper":{"title":"On the number of maximal intersecting k-uniform families and further applications of Tuza's set pair method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bal\\'azs Patk\\'os, Zolt\\'an L\\'or\\'ant Nagy","submitted_at":"2015-01-04T07:45:25Z","abstract_excerpt":"We study the function $M(n,k)$ which denotes the number of maximal $k$-uniform intersecting families $F\\subseteq \\binom{[n]}{k}$. Improving a bound of Balogh at al. on $M(n,k)$, we determine the order of magnitude of $\\log M(n,k)$ by proving that for any fixed $k$, $M(n,k) =n^{\\Theta(\\binom{2k}{k})}$ holds. Our proof is based on Tuza's set pair approach.\n  The main idea is to bound the size of the largest possible point set of a cross-intersecting system. We also introduce and investigate some related functions and parameters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00648","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"}