permutation

n 1: an event in which one thing is substituted for another [syn:

{substitution}, {transposition}, {replacement}, {switch}]

2: the act of changing the arrangement of a given number of

elements

3: complete change in character or condition: "the

permutations...taking place in the physical world"- Henry

Miller

4: act of changing the lineal order of objects in a group

permutation

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 that you can find an inverse

permutation that reverses the action of any given permutation.

A permutation is a {bijection}.

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.

(1995-04-10)