 
Summary: Disjoint Systems
Noga Alon
and Benny Sudakov
Department of Mathematics
Raymond and Beverly Sackler Faculty of Exact Sciences
Tel Aviv University, Tel Aviv, Israel
Abstract
A disjoint system of type (, , k, n) is a collection C = {A1, . . . , Am} of pairwise disjoint
families of ksubsets of an nelement 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,
limnDn(, , k)
n
k
1
=
1
2
.
