{"paper":{"title":"Spread approximations for forbidden intersections problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii, Dmitriy Zakharov","submitted_at":"2022-03-24T23:00:36Z","abstract_excerpt":"We develop a new approach to approximate families of sets, complementing the existing `$\\Delta$-system method' and `junta approximations method'. The approach, which we refer to as `spread approximations method', is based on the notion of $r$-spread families and builds on the recent breakthrough result of Alweiss, Lovett, Wu and Zhang for the Erd\\H os--Rado `Sunflower Conjecture'. Our approach can work in a variety of sparse settings.\n  To demonstrate the versatility and strength of the approach, we present several of its applications to forbidden intersection problems, including bounds on the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.13379","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/2203.13379/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"}