A set of sets W is called a sunflower if the pairwise intersections of all sets in W are the same. That is, there is some set S such that, for every distinct A,B ∈ W, A∩B = S. This includes the case where S is the empty set (so W is a set of disjoint sets).

Let f(k,r) be the largest number n such that there is a set U of n sets, each of cardinality k or less, and that U has no r-element subset that is a sunflower. It is a theorem that a largest such n always exists for any natural numbers k and r.

The Erdos-Rado sunflower conjecture states that for every r>2, there is some constant C(r) depending only on r, such that f(k,r) ≤ C(r)^k for all k.