相交族问题起源于著名的 Erdos-Ko-Rado 定理, 是极值组合学的重要研究内容. 在本文中, 我们利用 t-覆盖数研究了两类数学结构的相交族问题. 在第一部分, 我们研究了集合的 t-相交族问题, 刻画了基数较大的 t-相交族的结构. 在第二部分, 我们把集合中的结论推广到向量空间中, 刻画了向量空间的基数较大的 t-相交族的结构.

      Intersection problems originating from the famous Erdos-Ko-Rado theorem are very popular in extremal combinatorics. In this thesis, we study the intersection problems of two classical mathimatical objects by t-cover number. In the first part, we study t-intersecting families for sets, and characterize the structure of non-trivial t-intersecting families with large size. In the second part, we extend the structure of non-trivial t-intessecting families for sets to vector spaces. In other words, we characterize the structure of  non-trivial t-intersecting families with large size for vector spaces.