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Posets :: partitionLattice

partitionLattice -- computes the lattice of set-partitions of size $n$

Synopsis

Description

The partition lattice of order n is the lattice of setPartitions of the set {1,...,n} with ordering given by refinement. That is, the set-partition p is greater than or equal to the set-partition q if each part of p is contained in exactly one part of q.
i1 : partitionLattice 3

o1 = Poset{cache => CacheTable{...8...}                                                                                                                                                                                 }
           GroundSet => {{{1, 2, 3}}, {{1, 2}, {3}}, {{1, 3}, {2}}, {{1}, {2, 3}}, {{1}, {2}, {3}}}
           RelationMatrix => | 1 1 1 1 1 |
                             | 0 1 0 0 1 |
                             | 0 0 1 0 1 |
                             | 0 0 0 1 1 |
                             | 0 0 0 0 1 |
           Relations => {{{{1, 2, 3}}, {{1}, {2, 3}}}, {{{1, 2, 3}}, {{1, 3}, {2}}}, {{{1, 2, 3}}, {{1, 2}, {3}}}, {{{1, 2}, {3}}, {{1}, {2}, {3}}}, {{{1, 3}, {2}}, {{1}, {2}, {3}}}, {{{1}, {2, 3}}, {{1}, {2}, {3}}}}

o1 : Poset

See also

Ways to use partitionLattice :