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

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

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).

dCode retains ownership of the "Combinations with Repetition" source code. Except explicit open source licence (indicated Creative Commons / free), the "Combinations with Repetition" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Combinations with Repetition" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Combinations with Repetition" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

Reminder : dCode is free to use.

The copy-paste of the page "Combinations with Repetition" or any of its results, is allowed (even for commercial purposes) as long as you cite dCode!

Exporting results as a .csv or .txt file is free by clicking on the *export* icon

Cite as source (bibliography):

*Combinations with Repetition* on dCode.fr [online website], retrieved on 2023-10-01,

combination,repetition,repeats,tuple,uple,generator

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

© 2023 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback