Multilinear Polynomials And L-intersections

In this paper, we will discuss the size of a family F of subsets of [n] by employing the existing linear algebra methods. The paper is organized as follows:In Chapter 1, we introduce the history and research status of the intersecting families of [n]. Then, we give the basic concepts and properties. Finally, we show the main work.In Chapter 2 and 3, we get an improvement of Frankl-Wilson theorem and Alon-babai-suzuki theorem on the weakening conditions.In Chapter 4, we prove the same bound on the generalization of Alon-Babai-Suzuki theorem if we drop one condition n≥ s+max ki among r(s - r+1)≤ p - 1 and n≥ s+max ki.