{"paper":{"title":"Sunflowers and Ramsey problems for restricted intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","quant-ph"],"primary_cat":"math.CO","authors_text":"Barnab\\'as Janzer, Benny Sudakov, Kewen Wu, Zhihan Jin","submitted_at":"2025-04-21T17:46:21Z","abstract_excerpt":"Extremal problems on set systems with restricted intersections have been an important part of combinatorics in the last 70 year. In this paper, we study the following Ramsey version of these problems. Given a set $L\\subseteq \\{0,\\dots,k-1\\}$ and a family $\\mathcal{F}$ of $k$-element sets which does not contain a sunflower with $m$ petals whose kernel size is in $L$, how large a subfamily of $\\mathcal{F}$ can we find in which no pair has intersection size in $L$? We give matching upper and lower bounds, determining the dependence on $m$ for all $k$ and $L$. This problem also finds applications "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.15264","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.15264/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"}