Permutation



[pur-myoo-tey-shuh n] /ˌpɜr myʊˈteɪ ʃən/

noun
1.
the act of permuting or permutating; alteration; transformation.
2.
Mathematics.

/ˌpɜːmjʊˈteɪʃən/
noun
1.
(maths)

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
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).

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)

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