WordNet Dictionary- [n] act of changing the lineal order of objects in a group
- [n] complete change in character or condition; "the permutations...taking place in the physical world"- Henry Miller
- [n] the act of changing the arrangement of a given number of elements
- [n] an event in which one thing is substituted for another; "the replacement of lost blood by a transfusion of donor blood"
Webster's 1913 Dictionary\Per`mu*ta"tion\, n. [L. permutatio: cf. F.
permutation. See {Permute}.]
1. The act of permuting; exchange of the thing for another;
mutual transference; interchange.
The violent convulsions and permutations that have
been made in property. --Burke.
2. (Math.)
(a) The arrangement of any determinate number of things,
as units, objects, letters, etc., in all possible
orders, one after the other; -- called also
{alternation}. Cf. {Combination}, n., 4.
(b) Any one of such possible arrangements.
3. (Law) Barter; exchange.
{Permutation lock}, a lock in which the parts can be
transposed or shifted, so as to require different
arrangements of the tumblers on different occasions of
unlocking.
Computing Dictionary1. 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.
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