BUILT-IN MATHEMATICA SYMBOL

# 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:

 Out[1]=

Take the lowercase alphabet:

 Out[1]=

Exchange the first and last character:

 Out[2]=

Permute several characters:

 Out[3]=

Permute an expression under all elements of a group:

 Out[1]=