A set of elements of $P$ is called a chain if every pair of elements in the set are comparable.
i1 : D = divisorPoset 12; |
i2 : chains D
o2 = {{}, {1}, {1, 2}, {1, 2, 4}, {1, 2, 4, 12}, {1, 2, 6}, {1, 2, 6, 12},
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{1, 2, 12}, {1, 3}, {1, 3, 6}, {1, 3, 6, 12}, {1, 3, 12}, {1, 4}, {1, 4,
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12}, {1, 6}, {1, 6, 12}, {1, 12}, {2}, {2, 4}, {2, 4, 12}, {2, 6}, {2,
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6, 12}, {2, 12}, {3}, {3, 6}, {3, 6, 12}, {3, 12}, {4}, {4, 12}, {6},
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{6, 12}, {12}}
o2 : List
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With the input k, the method restricts to only chains of that length. In a divisorPoset, all chains of length $2$ describe exactly the divisor-multiple pairs.
i3 : chains(D, 2)
o3 = {{1, 2}, {1, 3}, {1, 4}, {1, 6}, {1, 12}, {2, 4}, {2, 6}, {2, 12}, {3,
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6}, {3, 12}, {4, 12}, {6, 12}}
o3 : List
|
The object chains is a method function.