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]

Moby Thesaurus II by Grady Ward, 1.0:

60 Moby Thesaurus words for "permutation":
   alteration, alternation, avatar, battledore and shuttlecock,
   catabolism, catalysis, commutation, consubstantiation, cooperation,
   counterchange, cross fire, displacement, exchange, give-and-take,
   heterotopia, innovation, interchange, intermutation, interplay,
   lex talionis, measure for measure, metabolism, metagenesis,
   metamorphism, metamorphosis, metastasis, metathesis,
   metempsychosis, modification, mutant, mutated form, mutation,
   mutual admiration, mutual support, mutual transfer, mutuality,
   novelty, quid pro quo, reciprocality, reciprocation, reciprocity,
   reincarnation, retaliation, something for something, sport,
   tit for tat, transanimation, transfiguration, transfigurement,
   transformation, transformism, translation, translocation,
   transmigration, transmogrification, transmutation, transposal,
   transposition, transubstantiation, vicissitude