The generating set method and its applications

Let $n$ and $k$ be two positive integers satisfying $n\geq 2k$. Let ${\mathcal A}$ be an intersecting family of $\binom{[n]}{k}$. The Erdős-Ko-Rado Theorem states that $|{\mathcal A}| \leq {n-1 \choose k - 1}.$ There are many generalizations of this theorem and many ways to study it have been generated as well. The generating set method, which has so far not received much attention, is a very efficient way of them. In this talk, we will introduces this method and give some of its applications.