The board / combinatorics / #20
Erdős Problem #20
sunflower conjecture
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(f(n,k)\) be minimal such that every \(F\) family of \(n\)-uniform sets with \(|F| \ge f(n,k)\) contains a \(k\)-sunflower.
Is it true that \(f(n,k) < c_k^n\) for some constant \(c_k>0\) and for all \(n > 0\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/20.Prize$1,000
Topicscombinatorics
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA332077
Original pageerdosproblems.com/20
Attempts
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The authoritative live page is OPEN - $1000 but lists sproutseeds, Rynaldos, and Lumantis under “Currently working on this problem” (accessed 2026-07-27), so the mandatory no-collision rule applies.
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