permutation (redirected from Cycle representation)

permutation

One possible combination of items out of a larger set of items. For example, with the set of numbers 1, 2 and 3, there are six possible permutations: 12, 21, 13, 31, 23 and 32.

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permutation

1. Maths

a. an ordered arrangement of the numbers, terms, etc., of a set into specified groups

b. a group formed in this way. The number of permutations of n objects taken r at a time is n&! / (n--r)&!

2. a fixed combination for selections of results on football pools

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permutation [‚pər·myə′tā·shən]

(mathematics)

A function which rearranges a finite number of symbols; more precisely, a one-to-one function of a finite set onto itself.

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(mathematics)

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 f(f'(x)) = f'(f(x)) = x.