2 problems

O'Neill's supersaturation conjecture. If $\mathcal{A}\subset 2^{[n]}$ consists of even-sized subsets and

Supersaturation conjecture. Let $n\geq 1$ and fix $3\leq s\leq 2^{\lfloor n/2\rfloor}-2^{\lfloor n/4\rfloor}$. If $[?]\subset 2^{[n]}$ consists of even-sized subsets with…