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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.

Permutation with Repetitions Generator

Counting Permutations with Repetitions

Answers to Questions

How to generate permutations with repetition?

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 do not matter.

Sets of n items are called tuples.

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 $.

How to remove the limit when computing permutations?

Permutations makes exponential values witch needs huge computing servers, so the generation must be paid.

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)

Source code

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