dilworthLattice -- computes the Dilworth lattice of a poset

Synopsis

Usage:

D = dilworthLattice P
Inputs:
- P, an instance of the type Poset,
Outputs:
- D, an instance of the type Poset, the Dilworth lattice of $P$

Description

The Dilworth lattice of $P$ is the lattice of maximum length (the dilworthNumber) antichains in $P$. Two such antichains have $A \leq B$ 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

Ways to use dilworthLattice :

dilworthLattice(Poset)

For the programmer

The object dilworthLattice is a method function.

dilworthLattice -- computes the Dilworth lattice of a poset

Synopsis

Description

See also

Ways to use dilworthLattice :

For the programmer