Permute

Permute[expr, perm]
permutes the positions of the elements of expr according to the permutation perm.

Permute[expr, gr]
returns the list of permuted forms of expr under the elements of the permutation group gr.

DetailsDetails

  • Permute works with any non-atomic expressions, operating on the first level of expressions.
  • Permute reorders the elements of an expression but never changes its length.
  • The permutation perm can be given in disjoint cyclic form or as a permutation list.
  • When perm is given in cyclic form Cycles[{cyc1, cyc2, ...}], a cycle moves the elements of expr in a cyclic manner so that is moved to position .
  • When perm is given as a permutation list, the result is equivalent to the use of Permute[expr, PermutationCycles[perm]].
  • A permutation group gr can be specified by generators, with head PermutationGroup, or in named form, with head SymmetricGroup, AlternatingGroup, ....

ExamplesExamplesopen allclose all

Basic Examples (3)Basic Examples (3)

Cyclic permutation of three elements in a list:

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Take the lowercase alphabet:

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Exchange the first and last character:

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Permute several characters:

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Permute an expression under all elements of a group:

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