An extension of the Erdos-Ko-Rado theorem to uniform set partitions

A (k, l)-partition is a set partition which has l blocks each of size k. Two (k, l)partitions P and Q are said to be partially t-intersecting if there exist blocks Pi in P and Q(j) in Q such that |P-i boolean AND Q(j) | >= t. In this paper we prove a version of the Erdos-KoRado theorem for partially 2-intersecting (k, l)-partitions. In particular, we show for l sufficiently large, the set of all (k, l)-partitions in which a block contains a fixed pair is the largest set of 2-partially intersecting (k, l)-partitions. For k = 3, we show this result holds for all l.