Some Results Related To The Erdos-Ko-Rado Theorem

The Erdos-Ko-Rado (EKR) theorem, which deals with the intersecting property in the lattice of subset, is the earliest result in researching the intersecting families of a finite set. It is also one of the most famous results in extreme set theory. In the past fifty years, The EKR theorem has been extended, simulated and refined.In this thesis, we present some other extensions of the EKR theorem under certain conditions, and study the theorem on multisets. Moreover, we give simple proofs for several famous theorems in extreme set theory by using our results. The main content of this thesis is arranged as follows.In Chapter1, we present some basic results about the EKR theorem, including background of the theorem.In Chapter2, we focus describing several proving methods of the EKR theorem.In Chapter3, we investigate the extension of the EKR theorem on antichains and multisets. At the same time, we give simple proofs for several famous theorems in extreme set theory by using the obtained results.In Chapter4, we explore simulations of the EKR theorem on the injection collection.In Chapter5, we present some applications of the EKR theorem.