The dominance lattice of partitions of $n$ is the lattice of partitions of $n$ under the dominance ordering. Suppose $p$ and $q$ are two partitions of $n$. Then $p$ is less than or equal to $q$ if and only if the $k$th partial sum of $p$ is at most the $k$th partial sum of $q$, where the partitions are extended with zeros, as needed.


For $n \leq 5$, the dominance lattice of $n$ is isomorphic to an appropriately long chain poset.




The object dominanceLattice is a method function.