The identity permutation of a set is the permutation that maps every element to itself. On elements labeled 1 through 
, it is 1, 2, ..., 
in one-line notation and can be written 
in permutation
cycle notation. It is the identity element
of the symmetric group 
under function composition.
Identity Permutation
See also
Identity Element, Permutation, Permutation Cycle, Permutation Group, Symmetric GroupExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Identity Permutation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IdentityPermutation.html