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Permutations with Repetition

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.

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Permutations with Repetition -

Tag(s) : Combinatorics

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# Permutations with Repetition

## Answers to Questions (FAQ)

### What is a permutation with repetition? (Definition)

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.

### How to generate permutations with repetition?

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.

### How to count 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 $3$.

### What is the Cartesian product of N identical sets?

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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Permutations with Repetition on dCode.fr [online website], retrieved on 2022-08-08, https://www.dcode.fr/permutations-with-repetitions

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