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The set of all subsets of the set S.
The set of subsets of the set S of size k. If k is larger than the cardinality
of S then the result will be empty.
The set of multisets consisting of k not necessarily distinct elements of
the set S.
The set of sequences of length k with elements from the set S.
The set of permutations (stored as sequences) of the elements of the set S.
The set of permutations (stored as sequences) of each of the subsets of
the set S of cardinality k.
The use of Subsets is illustrated in the construction of the Petersen
graph as the third Odd Graph. The nth Odd Graph has its vertices
in correspondence with the (n - 1)-element subsets of
{ 1 ... 2n - 1 }, and an edge between two vertices if
and only if their corresponding sets have empty intersection.
> V := Subsets( {1 .. 2*n-1}, n-1) where n is 3;
> V;
{
{ 1, 5 },
{ 2, 5 },
{ 1, 3 },
{ 1, 4 },
{ 2, 4 },
{ 3, 5 },
{ 2, 3 },
{ 1, 2 },
{ 3, 4 },
{ 4, 5 }
}
> E := { {u, v} : u,v in V | IsDisjoint(u, v) };
> Petersen := Graph< V | E >;
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