Tool to generate/count permutations with repetition. In Mathematics, a permutation with repetitions is an arrangement of items which can be repeated in various orders.

Permutations with Repetition - dCode

Tag(s) : Combinatorics

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Item permutations with repetition consist in the list of all possible arrangements of elements (which can be repeated) in any order.

__Example:__ `A,B,C` items be shuffled in 9 couples of 2 items: `A,A` `A,B` `A,C` `B,A` `B,B` `B,C`, `C,A`, `C,B`, `C,C`. The order of the items does matter (`A,B` and `B,A` are counted as 2 distinct permutations).

Sets of n items are called tuples.

The generation of permutations with repetitions can be carried out using several methods:

— From combinations with repetitions: for each combination with repetitions, generate their permutations. The set obtained is the list of permutations with repetition.

— From the combinations of choices: all the elements constitute a multiple choice, a permutation of size n is then a questionnaire of n questions with multiple choice. The set of choice combinations represents the list of permutations with repetition.

Counting permutations with repetition of $ k $ items in a list of $ N $ items is $ N^k $

__Example:__ There are $ 3^2 = 9 $ groups of permutations with repetition of $ 2 $ elements among $ 3 $.

In mathematics, the Cartesian product of N identical sets is equivalent to the generation of permutations with repetitions of N elements.

__Example:__ `{1, 2, 3} x {1, 2, 3}` returns the set of 9 permutations: `(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)`

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Cite as source (bibliography):

*Permutations with Repetition* on dCode.fr [online website], retrieved on 2024-09-13,

permutation,repetition,repeat,arrangement,tuple

https://www.dcode.fr/permutations-with-repetitions

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