meaning of permutation

1. The act of permuting; exchange of the thing for another; mutual transference; interchange.
2. 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.
3. Any one of such possible arrangements.
4. Barter; exchange.
5. permutation 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 ffx = ffx = x.
6. act of changing the lineal order of objects in a group

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