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

Combinations with Repetition - dCode

Tag(s) : Combinatorics

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Item combinations with repetition consist in generating the list of all possible combinations with elements that can be repeated.

__Example:__ `A,B,C` items are shuffled in 6 couples of 2 items: `A,A` `A,B` `A,C` `B,B` `B,C`, `C,C`. Without repetition, there would be only 3 couples `A,B`, `A,C` et `B,C`.

The sets of n elements are called tuples: `{1,2}` or `{1,2,3}` are tuples.

Counting repeated combinations of k items (sometimes called k-combination) in a list of N is noted $ \Gamma_n^k $ and $$ \Gamma_n^k = {n+k-1 \choose k} = \frac{(n+k-1)!}{k! (n-1)!} $$

The number of combinations with repeats of $ k $ items among $ N $ is equal to the number of combinations without repeats of $ k $ items among $ N + k - 1 $.

The calculation of the combinations generates an exponential number of values and the generator requires large calculation power on servers, these generations have therefore a cost (ask for a quote).

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

combination,repetition,repeats,tuple,uple,generator

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