# 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
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.

J. Henri Fabre
• This indicates the distinction between the permutation of letters and the transition of letters.

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.

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

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

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.

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

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

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

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

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
Word Origin
C14: from Latin permūtātiō, from permūtāre to change thoroughly; see mutation
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
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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### Word Value for permutation

0
19
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