{"paper":{"title":"Linear dependencies, polynomial factors in the Duke--Erd\\H os forbidden sunflower problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii, Fedor Noskov","submitted_at":"2024-10-08T15:59:27Z","abstract_excerpt":"We call a family of $s$ sets $\\{F_1, \\ldots, F_s\\}$ a \\textit{sunflower with $s$ petals} if, for any distinct $i, j \\in [s]$, one has $F_i \\cap F_j = \\cap_{u = 1}^s F_u$. The set $C = \\cap_{u = 1}^s F_u$ is called the {\\it core} of the sunflower. It is a classical result of Erd\\H os and Rado that there is a function $\\phi(s,k)$ such that any family of $k$-element sets contains a sunflower with $s$ petals. In 1977, Duke and Erd\\H os asked for the size of the largest family $\\mathcal{F}\\subset{[n]\\choose k}$ that contains no sunflower with $s$ petals and core of size $t-1$. In 1987, Frankl and F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.06156","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.06156/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}