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InversePermutation

InversePermutation[perm]
returns the inverse of permutation perm.
  • 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.
Inverse of a permutation:
Their product gives the identity permutation:
Some permutations, called involutions, are their own inverse:
Inverse of a permutation:
In[1]:=
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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]=
Invert a permutation:
On symbolic expressions other than permutations the result is given in terms of PermutationPower:
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