Generating all subsets of a finite set with disjoint unions

@article{Ellis2011GeneratingAS,
  title={Generating all subsets of a finite set with disjoint unions},
  author={David Ellis and Benny Sudakov},
  journal={J. Comb. Theory, Ser. A},
  year={2011},
  volume={118},
  pages={2319-2345}
}
If X is an n-element set, we call a family G ⊂ PX a k-generator for X if every x ⊂ X can be expressed as a union of at most k disjoint sets in G. Frein, Lévêque and Sebő [10] 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… CONTINUE READING