Erdős problem 447 · problems.science

How large can a union-free collection $\mathcal{F}$ of subsets of $[n]$ be? By union-free we mean there are no solutions to $A\cup B=C$ with distinct $A,B,C\in \mathcal{F}$ . Perhaps even $\lvert \mathcal{F}\rvert <(1+o(1))\binom{n}{\lfloor n/2\rfloor}?$

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/447.lean

Formal Conjectures

FormalConjectures/ErdosProblems/447.leanErdos447.erdos_447.parts.i1 lineExact file

1True ↔ (fun n => ↑(Erdos447.maxUnionFree n)) =o[Filter.atTop] fun n => 2 ^ n

SolvedStatement only, no proof

Proof manifests naming this Problem

Jayyhk Erdős Leanjayyhk:erdos:447
PLBY Lean proofsErdosProblems.Erdos447

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

Formalization
Erdős AI contributions wiki · 10 Feb, 2026
Machine
Aristotle
Open the source record

Continue

Start a contribution Browse the source files Open the collection entry

No current result

Proof manifests naming this Problem

Reported activity

Continue

Search problems.science