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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 = Relation Matrix: | 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 |

o2 : Poset

See also

Ways to use dilworthLattice :