partitions(Set,BasicList) -- Partitions of a set

Synopsis

Function: partitions
Usage:

par = partitions(S,L)
Inputs:
- S, a set,
- L, a basic list, a nonincreasing list of integers, or a partition
Outputs:
- par, a list,

Description

Given a set S and a partition L=\{l_1\geq l_2\cdots\}, the method returns the list of partitions of the set S of type L, i.e. representations of S as S=S_1\cup S_2\cup\cdots, where the S_i's are disjoint subsets of S having t_i elements.

i1 : partitions(set{1,2,3,4},{2,1,1})

o1 = {set {set {3}, set {4}, set {1, 2}}, set {set {1, 3}, set {4}, set {2}},
     ------------------------------------------------------------------------
     set {set {3}, set {2}, set {4, 1}}, set {set {1}, set {4}, set {2, 3}},
     ------------------------------------------------------------------------
     set {set {3}, set {1}, set {4, 2}}, set {set {1}, set {2}, set {4, 3}}}

o1 : List

i2 : partitions(set{a,b,c,d,e},new Partition from {3,2})

o2 = {set {set {a, b}, set {c, d, e}}, set {set {e, b}, set {c, d, a}}, set
     ------------------------------------------------------------------------
     {set {c, d, b}, set {a, e}}, set {set {c, a, e}, set {d, b}}, set {set
     ------------------------------------------------------------------------
     {d, a}, set {c, e, b}}, set {set {d, e}, set {c, a, b}}, set {set {c,
     ------------------------------------------------------------------------
     b}, set {d, a, e}}, set {set {d, e, b}, set {c, a}}, set {set {d, a, b},
     ------------------------------------------------------------------------
     set {c, e}}, set {set {c, d}, set {a, e, b}}}

o2 : List

Ways to use this method: