{"paper":{"title":"A new upper bound for the size of a sunflower-free family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"G\\'abor Heged\\\"us","submitted_at":"2017-02-09T13:48:15Z","abstract_excerpt":"We combine here Tao's slice-rank bounding method and Gr\\\"obner basis techniques and apply here to the Erd\\H{o}s-Rado Sunflower Conjecture.\n  Let $\\frac{3k}{2}\\leq n\\leq 3k$ be integers. We prove that if $\\mbox{$\\cal F$}$ be a $k$-uniform family of subsets of $[n]$ without a sunflower with 3 petals, then $$ |\\mbox{$\\cal F$}|\\leq 3{n \\choose n/3}. $$\n  We give also some new upper bounds for the size of a sunflower-free family in $2^{[n]}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02831","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"}