Erdős-Ko-Rado theorem

The Erdős-Ko-Rado theorem is a fundamental result in combinatorics, focusing on how large a family of sets can be when all sets share at least one common element. Specifically, it states that if you have a collection of subsets, each of a fixed size, from a larger set, and every pair of these subsets intersects, then the maximum size of this collection is achieved when all subsets contain a particular chosen element. In simple terms, to maximize the number of such intersecting subsets, they should all include one common element.