Erdős problem 1023 · problems.science

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 $F(n)\sim c \frac{2^n}{n^{1/2}}?$

Sources

Browse retained paths and inspect the exact material available for this Problem.

3 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

1023.lean

Retained formal statement2 of 3

Erdős and Kleitman proved in unpublished work that $F(n)\asymp \frac{2^n}{n^{1/2}}.$ ([Er71] has an exponent of $3/2$ , but this is presumably a typo.)

FormalConjectures/ErdosProblems/1023.leanErdos1023.erdos_1023.variants.erdos_kleitman1 lineExact file

1(fun n => ↑(Erdos1023.F n)) =Θ[Filter.atTop] fun n => 2 ^ n / ↑n ^ (1 / 2)

SolvedStatement only, no proof

Sources

Search problems.science