Tool to generate arrangements with repetitions. In Mathematics, a arrangement with repetitions is a arrangements of items which can be repeated.

Arrangements with Repetition - dCode

Tag(s) : Combinatorics

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Item arrangements with repetition (also called k-permutations with repetition) are the list of all possible arrangements of elements (each can be repeated) in any order.

__Example:__ `X,Y,Z` items be shuffled in 9 couples of 2 items: `X,X` `X,Y` `X,Z` `Y,X` `Y,Y` `Y,Z`, `Z,X`, `Z,Y`, `Z,Z`. The order of the items do not matter.

Sets of $ n $ items are called tuples or n-uplets.

Counting repeated arrangements of $ k $ items in a list of $ N $ is $ N^k $

The calculations of arrangements increase exponentially and quickly require large computing servers, so the free generations are limited.

In mathematics, the Cartesian product of N identical sets is the name given the generation of arrangements with repetitions of 2 elements among N.

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

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

arrangement,repetition,repeats,order,tuple,uple,generator

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

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