permutation
NounWordNet 3.0
Noun (4)
- an event in which one thing is substituted for another“the replacement of lost blood by a transfusion of donor blood”Synonyms: substitutiontranspositionreplacementswitch
- the act of changing the arrangement of a given number of elements
- complete change in character or condition“the permutations...taking place in the physical world — Henry Miller”
- act of changing the lineal order of objects in a group
Webster's Dictionary (GCIDE)
1.The act of permuting; exchange of the thing for another; mutual transference; interchange. [1913 Webster]
The violent convulsions and permutations that have been made in property.— Burke.[1913 Webster]
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. [1913 Webster]
3.(Law) Barter; exchange. [1913 Webster]
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. [1913 Webster]
Free On-line Dictionary of Computing
<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)