Erdős problem 272

Let $N\geq 1$ . What is the largest $t$ such that there are $A_1,\ldots,A_t\subseteq \{1,\ldots,N\}$ with $A_i\cap A_j$ a non-empty arithmetic progression for all $i\neq j$ ?

Sources

The source's own material, retained exactly.

4 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

272.lean

Retained formal statement2 of 4

Simonovits and Sós have shown that $t\ll N^2$ .

FormalConjectures/ErdosProblems/272.leanErdos272.erdos_272.variants.isBigO_sq1 lineExact file

1(fun N => ↑(Erdos272.maxArithInterCard N)) =O[Filter.atTop] fun N => ↑N ^ 2

SolvedStatement only, no proof