5 problems

Cross-intersecting set-system conjecture. For every fixed $k>0$, if $|L|=k$ and $\mathcal A,\mathcal B$ are $L$-cross-intersecting, then there exist $\mathcal R\subseteq\mathcal A$…

Parallel $k$-partition conjecture. For every fixed integer $k>1$,

Parallel 2-partition conjecture. Then

Log-rank conjecture. For every function $f: \mathcal X \times \mathcal Y \to \{0,1\}$,

Let $f: \{0,1\}^n \to \{0,1\}$ be a Boolean function, and let $\operatorname{spar}(f)=r$ be its sparsity, namely the number of nonzero coefficients in its unique multilinear polyno…