A set of elements of $P$ is called an antichain if no two distinct elements of the set are comparable.
i1 : D = divisorPoset 12; |
i2 : antichains D
o2 = {{}, {1}, {2}, {2, 3}, {3}, {3, 4}, {4}, {4, 6}, {6}, {12}}
o2 : List
|
With the input k, the method restricts to only antichains of that length. In a divisorPoset, all chains of length $2$ describe exactly the non-divisor-multiple pairs.
i3 : antichains(D, 2)
o3 = {{2, 3}, {3, 4}, {4, 6}}
o3 : List
|
Since every distinct pair of vertices in a chain is comparable, the only antichains of a chain are the singleton sets and the empty set.
i4 : antichains chain 5
o4 = {{}, {1}, {2}, {3}, {4}, {5}}
o4 : List
|
The object antichains is a method function.