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SchurRings :: partitions(Set,BasicList)

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

Synopsis

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

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

o2 : List