On non-empty cross-intersecting families

Chao Shi, Peter Frankl, Jianguo Qian

Let $2^{[n]}$ and $\left(\genfrac{}{}{0ex}{}{[n]}{i}\right)$ be the power set and the class of all $i$-subsets of $\{1,2,\cdots ,n\}$, respectively. We call two families $\mathcal{A}$ and $\mathcal{B}$ cross…