The Collaborative International Dictionary of English v.0.48:

Permutation \Per`mu*ta"tion\ (p[~e]r`m[-u]"t[=a]"sn[u^]n), n.
   [L. permutatio: cf. F. permutation. See Permute.]
   1. The act of permuting; exchange of the thing for another;
      mutual transference; interchange.
      [1913 Webster]

            The violent convulsions and permutations that have
            been made in property.                --Burke.
      [1913 Webster]

   2. (Math.)
      (a) The arrangement of any determinate number of things,
          as units, objects, letters, etc., in all possible
          orders, one after the other; -- called also
          alternation. Cf. Combination, n., 4.
      (b) Any one of such possible arrangements.
          [1913 Webster]

   3. (Law) Barter; exchange.
      [1913 Webster]

   Permutation lock, a lock in which the parts can be
      transposed or shifted, so as to require different
      arrangements of the tumblers on different occasions of
      unlocking.
      [1913 Webster]

WordNet (r) 3.0 (2006):

permutation
    n 1: an event in which one thing is substituted for another;
         "the replacement of lost blood by a transfusion of donor
         blood" [syn: substitution, permutation,
         transposition, replacement, switch]
    2: the act of changing the arrangement of a given number of
       elements
    3: complete change in character or condition; "the
       permutations...taking place in the physical world"- Henry
       Miller
    4: act of changing the lineal order of objects in a group

The Free On-line Dictionary of Computing (19 January 2023):

permutation

    1. An ordering of a certain number of elements
   of a given set.

   For instance, the permutations of (1,2,3) are (1,2,3) (2,3,1)
   (3,1,2) (3,2,1) (1,3,2) (2,1,3).

   Permutations form one of the canonical examples of a "group"
   - they can be composed and you can find an inverse permutation
   that reverses the action of any given permutation.

   The number of permutations of r things taken from a set of n
   is

    n P r = n! / (n-r)!

   where "n P r" is usually written with n and r as subscripts
   and n! is the factorial of n.

   What the football pools call a "permutation" is not a
   permutation but a combination - the order does not matter.

   2. A bijection for which the domain and range are the
   same set and so

   f(f'(x)) = f'(f(x)) = x.

   (2001-05-10)