# 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)

Tagged: p

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