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

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]

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)

PERMUTATION, civil law. Exchange; barter. 
     2. This contract is formed by the consent of the parties, but delivery 
is indispensable; for, without it, it mere agreement. Dig. 31, 77, 4; Code, 
4, 64, 3. 
     3. Permutation differs from sale in this, that in the former a delivery 
of the articles sold must be made, while in the latter it is unnecessary. It 
agrees with the contract of sale, however, in the following particulars: 1. 
That he to whom the delivery is made acquires the right or faculty of 
prescribing. Dig. 41, 3, 4, 17. 2. That the contracting parties are bound to 
guaranty to each other the title of the things delivered. Code, 4, 64, 1. 3. 
That they are bound to take back the things delivered, when they have latent 
defects which they have concealed. Dig. 21, 1, 63. See Aso & Man. Inst. B. 
2, t. 16, c. 1; Nutation; Transfer.