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permutation

[pur-myoo-tey-shuh n] /ˌpɜr myʊˈteɪ ʃən/
noun
1.
the act of permuting or permutating; alteration; transformation.
2.
Mathematics.
  1. 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.
  2. any of the resulting arrangements or groups.
    Compare combination (def 8b).
Origin of permutation
1325-1375
1325-75; Middle English permutacioun (< Middle French permutacion) < Latin permūtātiōn- (stem of permūtātiō) thoroughgoing change. See per-, mutation, permute
Related forms
permutational, adjective
permutationist, noun
Synonyms
1. modification, transmutation, change.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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Examples from the Web for permutation
Historical Examples
  • The first permutation makes the second seem very probable, although I cannot as yet conceive a means of realizing it.

    Bramble-bees and Others J. Henri Fabre
  • This indicates the distinction between the permutation of letters and the transition of letters.

    The English Language Robert Gordon Latham
  • Nevertheless, it is much easier to give the child a vivid impression of them by the permutation of parts than by explanation.

  • The economic reform wrought is largely of the nature of a permutation in the methods of conspicuous waste.

  • Let this be learned to perfection, backwards and forwards, or by permutation of words, and repeated the next day.

    The Mystic Will Charles Godfrey Leland
  • This permutation is made very convenient by the sentences being printed in sections which may be moved about and combined at will.

  • We may thus select the four coins in one hundred ways, and the four removed may be arranged by permutation in twenty-four ways.

    Amusements in Mathematics Henry Ernest Dudeney
  • This permutation was not quite unnatural; for Wilhelm and Laertes did resemble one another, though in a very distant manner.

  • He is not a permutation and combination of old elements, transferred through the parents.

  • It is clear how very different the results would become by the permutation and combination of these diverse factors.

    Life Movements in Plants Sir Jagadis Chunder Bose
British Dictionary definitions for permutation

permutation

/ˌpɜːmjʊˈteɪʃən/
noun
1.
(maths)
  1. 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
  2. a group formed in this way. The number of permutations of n objects taken r at a time is n!/(nr)! nPr Compare combination (sense 6)
2.
a combination of items made by reordering
3.
an alteration; transformation
4.
a fixed combination for selections of results on football pools Usually shortened to perm
Derived Forms
permutational, adjective
Word Origin
C14: from Latin permūtātiō, from permūtāre to change thoroughly; see mutation
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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Word Origin and History for permutation
n.

mid-14c., from Old French permutacion "change, shift" (14c.), from Latin permutationem (nominative permutatio) "a change, alteration, revolution," noun of action from past participle stem of permutare "change thoroughly, exchange," from per- "thoroughly" (see per) + mutare "to change" (see mutable).

Online Etymology Dictionary, © 2010 Douglas Harper
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permutation in Technology

mathematics
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)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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