partition lattice


The partition lattice (or lattice of partitions) Πn is the lattice of set partitionsMathworldPlanetmathPlanetmath (http://planetmath.org/Partition) of the set [n]={1,…,n}. The partial orderMathworldPlanetmath on Πn is defined by refinement, setting x≤y if any only if each cell of x is contained in a cell of y.

If n<3, then Πn is a chain. But Π3 is not even a distributive latticeMathworldPlanetmath:

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