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Posets :: ncpLattice

ncpLattice -- computes the non-crossing partition lattice of set-partitions of size $n$

Synopsis

Description

The non-crossing partition lattice of order n is the lattice of ncPartition (missing documentation)s of the set {0,...,n-1} with ordering given by refinement. That is, the non-crossing partition p is greater than or equal to the non-crossing partition q if each part of p is contained in exactly one part of q.
i1 : ncpLattice 3

o1 = Poset{cache => CacheTable{...8...}                                                                     }
           GroundSet => {012, 0/12, 02/1, 01/2, 0/1/2}
           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 => {{012, 0/12}, {012, 02/1}, {012, 01/2}, {0/12, 0/1/2}, {02/1, 0/1/2}, {01/2, 0/1/2}}

o1 : Poset

See also

Ways to use ncpLattice :