Disjoint Systems (Extended Abstract)

Systems (Extended Abstract) Noga Alon ∗ Benny Sudakov Department of Mathematics Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv, Israel A disjoint system of type (∀, ∃, k, n) is a collection C = {A1, . . . , Am} of pairwise disjoint families of k-subsets of an n-element set satisfying the following condition. For every ordered pair Ai and Aj of distinct members of C and for every A ∈ Ai there exists a B ∈ Aj that does not intersect A. Let Dn(∀, ∃, k) denote the maximum possible cardinality of a disjoint system of type (∀, ∃, k, n). It is shown that for every fixed k ≥ 2, limn→∞Dn(∀, ∃, k) n k −1 = 1 2 . This settles a problem of Ahlswede, Cai and Zhang. Several related problems are considered as well.

• Type: Conference
• Year: 1993
• Where: FIWAC
• Authors: Noga Alon, Benny Sudakov
• Keywords: Cryptology, FIWAC 1993, Pairwise Disjoint Families, Tel Aviv, Tel Aviv University