A partition lattice is a mathematical structure that represents the ways to divide a set into non-empty, disjoint subsets, known as partitions. Each partition can be thought of as a grouping of elements, and the lattice is formed by considering these partitions as nodes connected by relationships defined by set inclusion. The partition lattice showcases the inherent structure of these partitions and how they can be combined or refined, leading to an understanding of their ordering.
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