  If X is an n-element set, we call a family G of subsets of X a k-generator
for X if every subset of X can be expressed as a union of at most k disjoint
sets in G. Frein, Leveque and Sebo conjectured that for n > 2k, the smallest
k-generators for X are obtained by taking a partition of X into classes of
sizes as equal as possible, and taking the union of the power-sets of the
classes. We prove this conjecture for all sufficiently large n when k = 2, and
for n a sufficiently large multiple of k when k > 2.
