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based on an earlier version of the Wolfram Language.
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Subsets and Permutations
Permutations list permutations of a set of integers
SignaturePermutation sign or parity of a permutation
InversePermutation apply an inverse permutation
Inversions number of inversions
Index index of a permutation
PermutationGraph graph for a permutation
PermutationType  ▪ Runs  ▪ Eulerian  ▪ ...
CyclicGroup group of circular shift permutations
Orbits orbits induced by the action of the group
CycleIndex cycle index of a group of permutations
Strings subsets with repeating elements
BinarySubsets enumerate subsets
KSubsets subsets with elements
ToCycles find cycles for a permutation
HideCycles represent the cycle in canonical form