Lattice of Partitions of a 4-Element Set - Tilman Piesk

Lattice of Partitions

This picture by Tilman Piesk shows the 15 partitions of a 4-element set, ordered by refinement. Finer partitions are connected to coarser ones by lines going down. In the finest partition, on top, each of the 4 elements is in its own subset. In the coarsest one, on bottom, all 4 elements are in the same subset.