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Posets :: dilworthLattice

dilworthLattice -- computes the Dilworth lattice of a poset

Synopsis

Description

The Dilworth lattice of P is the lattice of maximum length (the dilworthNumber) antichains in P. Two such antichains have A ≤B if and only if every member of A is less than or equal (in P) to some member of B.
i1 : P = poset {{0, 2}, {1, 2}, {1, 3}, {2, 5}, {3, 4}, {3, 5}};
i2 : dilworthLattice P

o2 = Poset{cache => CacheTable{...3...}                                                                                                                                                                                                                                             }
           GroundSet => {{0, 4}, {0, 1}, {0, 3}, {2, 4}, {2, 3}, {5, 4}}
           RelationMatrix => | 1 0 0 1 0 1 |
                             | 1 1 1 1 1 1 |
                             | 1 0 1 1 1 1 |
                             | 0 0 0 1 0 1 |
                             | 0 0 0 1 1 1 |
                             | 0 0 0 0 0 1 |
           Relations => {{{0, 4}, {2, 4}}, {{0, 4}, {5, 4}}, {{0, 1}, {0, 4}}, {{0, 1}, {0, 3}}, {{0, 1}, {2, 4}}, {{0, 1}, {2, 3}}, {{0, 1}, {5, 4}}, {{0, 3}, {0, 4}}, {{0, 3}, {2, 4}}, {{0, 3}, {2, 3}}, {{0, 3}, {5, 4}}, {{2, 4}, {5, 4}}, {{2, 3}, {2, 4}}, {{2, 3}, {5, 4}}}

o2 : Poset

See also

Ways to use dilworthLattice :