Permutation

:See permutation (music) for the application of this concept to music.

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In mathematics, especially in abstract algebra and related areas, a permutation is a bijection from a finite set X onto itself.

Related Topics:
Mathematics - Abstract algebra - Bijection - Finite - Set

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In combinatorics, the term permutation has a traditional meaning, which is used to include ordered lists without repetition, but not exhaustive (so of less than maximum length).

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The concept of a permutation expresses the idea that distinguishable objects may be arranged in various different orders. For instance, with the numbers one to six, each possible order makes a list of the numbers, without repetitions. One such permutation is: (3, 4, 6, 1, 2, 5).

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There are a number of ways in which the permutation concept may be defined more formally. A permutation is an ordered sequence containing each symbol from a set once and only once; neither (1, 2, 2, 3, 4, 5, 6) nor (1, 2, 4, 5, 6) are permutations. One can therefore point to the essential difference between a permutation and a set: the elements of a permutation are arranged in a specified order.

Related Topics:
Sequence - Set

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