On finite Δ-systems II

Abstract A Δ(k) system is a family F of k distinct sets which have pairwise the same intersection. A weak Δ(k) system is a family F of k distinct sets such that | F þ G | = t for some non-negative integer t and all F,G ϵ F , F ≠ G. In this paper we study some functions related to these Δ-systems. In particular α(n,k) = max{| F | : | F | = n ∀ F ϵ F , F ⊅ weak Δ(k)} then α(3,3) = 10, α(m + n, k) ⩾ α (m, k) α(n, k) and α (n, 3) > c5 n 2