ULethbridge Number Theory and Combinatorics Seminar: Sarobidy Razafimahatratra

The Erdős-Ko-Rado (EKR) theorem states that if n and k are two positive integers such that n≥2k and F is a family of k-subsets of {1,2,…,n} such that A∩B≠∅, for all A,B∈F, then |F|⩽(n−1k−1). Moreover, if n⩾2k+1, then equality holds if and only if there exists a∈{1,2,…,n} such that F={A⊂{1,2,…,n}:|A|=k and a∈A}.

The Erdős-Ko-Rado theorem can sometimes be extended to other combinatorical objects, provided that a well-defined notion of intersection between objects exists. In this talk, I will give some examples where the EKR theorem can be generalized to other objects. Then, I will present some recent EKR type results on transitive permutation groups.