Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Mathematica > Mathematics and Algorithms > Discrete Mathematics > Permutations > InversePermutation >
BUILT-IN MATHEMATICA SYMBOLTutorials »|See Also »|More About »

InversePermutation

InversePermutation[perm]
returns the inverse of permutation perm.
MORE INFORMATION
  • The product of a permutation with its inverse gives the identity permutation.
  • Every permutation has a uniquely defined inverse.
  • The support of a permutation is the same as the support of its inverse.
EXAMPLESCLOSE ALL
Basic Examples   (2)
Inverse of a permutation:
Their product gives the identity permutation:
Some permutations, called involutions, are their own inverse:
Inverse of a permutation:
In[1]:=
Click for copyable input
Out[1]=
Their product gives the identity permutation:
In[2]:=
Click for copyable input
Out[2]=
 
Some permutations, called involutions, are their own inverse:
In[1]:=
Click for copyable input
Out[1]=
Scope   (1)
Invert a permutation:
Generalizations & Extensions   (1)
On symbolic expressions other than permutations the result is given in terms of PermutationPower:
Properties & Relations   (4)
InversePermutation is equivalent to PermutationPower with exponent :
Inverting a permutation is equivalent to reversing its cycles:
For a permutation of finite degree, its inverse can always be obtained as the power with a positive integer:
Ordering gives the inverse of a permutation list:
New in 8
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF