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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Permutations with Repetition
Permutation with Repetitions Generator
Counting Permutations with Repetitions
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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