A new generalization of the Erdös-Ko-Rado theorem

Abstract Let A and B be systems of k and l element subsets of an n element set respectively. Suppose that A ∩ B ≠ ⊘ for all A ϵ A , B ϵ B . It is proved that | A | | B ⩽ n −1 k −1 n −1 l −1 , whenever n ⩾ 2k + l − 2 (k ⩾ l).