Problem dossier · Combinatorics
Sunflower conjecture
Erdős–Rado: any family of more than C(r)^w sets, each of size w, contains an r-sunflower (r sets with identical pairwise intersections). The conjecture puts C(r) independent of w.
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Status
Open. Alweiss–Lovett–Wu–Zhang (2019) reduced the classical w! bound to roughly (r log w)^w; the constant-base conjecture stands.
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The Angle of Attack
Construct large sunflower-free families for small r and w to test tightness; probe the entropy/spread technique's limits computationally.
Tags: set systems · sunflowers · extremal · spread
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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Related Problems
More open problems in Combinatorics and adjacent territory.
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