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Permute[expr,perm]
Permute 2 2 5 5 Child Custody Schedule
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.
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- Permute works with any nonatomic 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 {p1,p2,…} moves the elements of expr in a cyclic manner so that expr[[pi]] is moved to position pi+1.
- 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, ….
Basic Examples(3)
Cyclic permutation of three elements in a list:
Take the lowercase alphabet:
Exchange the first and last character:
Permute several characters:
Permute an expression under all elements of a group:
Scope(3)
Permute the parts of an expression:
Permute the parts of an expression under all elements of a group: Csimsoft trellis pro 16 5 41.
Give a permutation in list form. The length of the expression does not change:
Applications(1)
The eight possible rotations and reflections of a square:
Properties & Relations(5)
Permute never changes the number of parts of an expression. It simply reorders them:
However, Part can change the number of parts:
When applied to the identity permutation list, Permute is the inverse of PermutationReplace:
Permute can also be used as an alternative to PermutationList:
When all parts of the expression are different, the permutation can be uniquely recovered:
Permute 2 2 5 5 Esv
Permute is a right action with respect to the product of permutations:
Permute 2 2 5 5g
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Introduced in 2010