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Posets :: flagPoset

flagPoset -- computes the subposet of specified ranks of a ranked poset

Synopsis

Description

The flag poset with respect to a list of rank indices is the subposet induced by the specified ranks. The maximal chains of the flag poset can be computed with the flagChains method.
i1 : P = booleanLattice 4;
i2 : rankFunction P

o2 = {0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4}

o2 : List
i3 : flagPoset(P, {2,3})

o3 = Poset{cache => CacheTable{}                                                                                                                                                                }
           GroundSet => {0011, 0101, 0110, 0111, 1001, 1010, 1011, 1100, 1101, 1110}
           RelationMatrix => | 1 0 0 1 0 0 1 0 0 0 |
                             | 0 1 0 1 0 0 0 0 1 0 |
                             | 0 0 1 1 0 0 0 0 0 1 |
                             | 0 0 0 1 0 0 0 0 0 0 |
                             | 0 0 0 0 1 0 1 0 1 0 |
                             | 0 0 0 0 0 1 1 0 0 1 |
                             | 0 0 0 0 0 0 1 0 0 0 |
                             | 0 0 0 0 0 0 0 1 1 1 |
                             | 0 0 0 0 0 0 0 0 1 0 |
                             | 0 0 0 0 0 0 0 0 0 1 |
           Relations => {{0011, 0111}, {0011, 1011}, {0101, 0111}, {0101, 1101}, {0110, 0111}, {0110, 1110}, {1001, 1011}, {1001, 1101}, {1010, 1011}, {1010, 1110}, {1100, 1101}, {1100, 1110}}

o3 : Poset
i4 : flagPoset(P, {1})

o4 = Poset{cache => CacheTable{}                }
           GroundSet => {0001, 0010, 0100, 1000}
           RelationMatrix => | 1 0 0 0 |
                             | 0 1 0 0 |
                             | 0 0 1 0 |
                             | 0 0 0 1 |
           Relations => {}

o4 : Poset

See also

Ways to use flagPoset :