The board / combinatorics / #1023
Erdős Problem #1023
SOLVED LEANdatabase updated 2026-02-10
Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
`F n` is the maximal size of a family of subsets of \(\{1,\ldots,n\}\) such that no set in this family is the union of other members of the family.
Let \(F(n)\) be the maximal size of a family of subsets of \(\{1,\ldots,n\}\) such that no set in this family is the union of other members of the family. Is it true that there is a constant \(c>0\) such that \[F(n)\sim c \frac{2^n}{n^{1/2}}?\] Hunter observes in the comments that this follows from the solution to [447], which implies \(F(n)\sim \binom{n}{n/2}\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/1023.Prizenone
Topicscombinatorics
Statement in LeanFormal Conjectures
Solution in Leanyes
OEISA347025
Original pageerdosproblems.com/1023
Attempts
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