A new short proof of the EKR theorem

A family F is intersecting if F ∩ F ′ ≠ ∅ whenever F , F ′ ∈ F . Erdős, Ko, and Rado (1961) [6] showed that(1) | F | ⩽ ( n − 1 k − 1 ) holds for an intersecting family of k-subsets of [ n ] : = { 1 , 2 , 3 , … , n } , n ⩾ 2 k . For n > 2 k the only extremal family consists of all k-subsets containing a fixed element. Here a new proof is presented by using the Katonaʼs shadow theorem for t-intersecting families.