The largest set partitioned by a subfamily of a cover

Define [lambda](n) to be the largest integer such that for each set A of size n and cover J of A, there exist B [subset of or equal to] A and G [subset of or equal to] J such that |B| = [lambda](n) and the restriction of G to B is a partition of B. It is shown that when n [ges] 3. The lower bound is proved by a probabilistic method. A related probabilistic algorithm for finding large sets partitioned by a subfamily of a cover is presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28503/1/0000300.pd