[pur-myoo-tey-shuhn] Pronunciation Key | 1. | the act of permuting or permutating; alteration; transformation. |
| 2. | Mathematics.
|
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2006.
| per·mu·ta·tion
(pûr'myŏŏ-tā'shən) Pronunciation Key
n.
per'mu·ta'tion·al adj. |
The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2006 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
permutation
| permutation | |
noun | |
| 1. | an event in which one thing is substituted for another; "the replacement of lost blood by a transfusion of donor blood" [syn: substitution] |
| 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 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)
Permutation
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.
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