The non-crossing partition lattice of order $n$ is the lattice of ncPartitions of the set $\{0,\ldots,n-1\}$ 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 = Relation Matrix: | 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 | o1 : Poset |
The object ncpLattice is a method function.