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.
i1 : D = dominanceLattice 6;
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i2 : closedInterval(D, {2,2,1,1}, {4,2})
o2 = Relation Matrix: | 1 0 0 0 0 0 0 |
| 1 1 0 0 0 0 0 |
| 1 0 1 0 0 0 0 |
| 1 1 1 1 0 0 0 |
| 1 1 1 1 1 0 0 |
| 1 1 1 1 0 1 0 |
| 1 1 1 1 1 1 1 |
o2 : Poset
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For n ≤5, the dominance lattice of n is isomorphic to an appropriately long chain poset.
i3 : dominanceLattice 2 == chain 2
o3 = true
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i4 : dominanceLattice 3 == chain 3
o4 = true
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i5 : dominanceLattice 4 == chain 5
o5 = true
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i6 : dominanceLattice 5 == chain 7
o6 = true
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