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

Synopsis

Usage:

P = partitionLattice n
Inputs:
- n, an integer, the size of the set to partition
Outputs:
- P, an instance of the type Poset,

Description

The partition lattice of order $n$ is the lattice of setPartitions of the set $\{1,\ldots,n\}$ 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 = 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

Ways to use partitionLattice :

partitionLattice(ZZ)

For the programmer

The object partitionLattice is a method function.

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

Synopsis

Description

See also

Ways to use partitionLattice :

For the programmer