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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Arrangements with Repetition on dCode.fr [online website], retrieved on 2024-11-21,