the act of permuting or permutating; alteration; transformation.
the act of changing the order of elements arranged in a particular order, as abc into acb, bac, etc., or of arranging a number of elements in groups made up of equal numbers of the elements in different orders, as a and b in ab and ba; a one-to-one transformation of a set with a finite number of elements.
any of the resulting arrangements or groups. Compare combination ( def 8b ).

1325–75; Middle English permutacioun (< Middle French permutacion) < Latin permūtātiōn- (stem of permūtātiō) thoroughgoing change. See per-, mutation, permute

permutational, adjective
permutationist, noun

1. modification, transmutation, change. Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
permutation (ˌpɜːmjʊˈteɪʃən)
1.  maths
 a.  an ordered arrangement of the numbers, terms, etc, of a set into specified groups: the permutations of a, b, and c, taken two at a time, are ab, ba, ac, ca, bc, cb
 b.  Compare combination nPr a group formed in this way. The number of permutations of n objects taken r at a time is n!/(n--r)!
2.  a combination of items made by reordering
3.  an alteration; transformation
4.  Usually shortened to: perm a fixed combination for selections of results on football pools
[C14: from Latin permūtātiō, from permūtāre to change thoroughly; see mutation]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

mid-14c., from O.Fr. permutacion (14c.), from L. permutationem (nom. permutatio), from permutatus, pp. of permutare "change thoroughly, exchange," from per- "thoroughly" + mutare "to change" (see mutable).
Online Etymology Dictionary, © 2010 Douglas Harper
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Computing Dictionary

permutation definition

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.

The Free On-line Dictionary of Computing, © Denis Howe 2010
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Example sentences
Right now, moviegoers are riding a wave of movies that feature insects in every
  possible permutation.
The interesting permutation in this backchannel backlash, to me, is that it was
  conducted silently.
The reason is that every possible permutation needs to be looked at in order to
  find the best.
Each is a permutation of the other, with no two alike.
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