The Upper Limit Of L-intersections

In this paper, we introduce the method of the proof of theorem 1.11 and 1.14 in reference [1]. Further more, we change some conditions and generalized the theorem to get upper bounds of subset intersecting families of a finite set.This paper has 4 parts. The first part introduces the related conditions of Sperner theorem and Erdos-Ko-Rado theorem and the main work. The second part gives some mathematical notations, concepts as well as some theorems of intersecting families that will be used in this paper, including the theorems and the proofs. The last part gives the brief summary of this paper.