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]

The Collaborative International Dictionary of English v.0.48:

Alternation \Al`ter*na"tion\, n. [L. alternatio: cf. F.
   alternation.]
   1. The reciprocal succession of things in time or place; the
      act of following and being followed by turns; alternate
      succession, performance, or occurrence; as, the
      alternation of day and night, cold and heat, summer and
      winter, hope and fear.
      [1913 Webster]

   2. (Math.) Permutation.
      [1913 Webster]

   3. The response of the congregation speaking alternately with
      the minister. --Mason.
      [1913 Webster]

   Alternation of generation. See under Generation.
      [1913 Webster]

WordNet (r) 3.0 (2006):

alternation
    n 1: successive change from one thing or state to another and
         back again; "a trill is a rapid alternation between the two
         notes"

Moby Thesaurus II by Grady Ward, 1.0:

97 Moby Thesaurus words for "alternation":
   Lissajous figure, back-and-forth, battledore and shuttlecock, beat,
   chain, coaction, coming and going, commutation,
   complementary distribution, concurrence, consecution, cooperation,
   counterchange, cross fire, cyclicalness, ebb and flow, engagement,
   exchange, fluctuation, flux and reflux, give-and-take, interaction,
   interchange, intercommunication, intercourse, interlacing,
   intermeshing, intermittence, intermittency, intermutation,
   interplay, intertwining, interweaving, interworking, lex talionis,
   measure for measure, mesh, meshing, meter, mutual admiration,
   mutual support, mutual transfer, mutuality, order, oscillation,
   pendulation, pendulum motion, periodicalness, periodicity,
   permutation, piston motion, progression, pulsation, quid pro quo,
   reappearance, reciprocality, reciprocation, reciprocity,
   recurrence, regular wave motion, reoccurrence, repetition,
   retaliation, return, reversion, rhythm, rhythmic play, rotation,
   row, seasonality, seesaw, seesawing, sequel, sequence, series,
   shifting, shuffling, sine wave, something for something,
   succession, teeter, teeter-totter, teeter-tottering, teetering,
   tit for tat, to-and-fro, tottering, train, transposal,
   transposition, undulation, ups and downs, vacillation, variation,
   vicissitude, wavering, wigwag