Tool to count and generate partial k-permutations. In Mathematics, a partial permutation (or k-permutation) is an ordered list of items. It consists in permutations of each combination.

k-Permutations - dCode

Tag(s) : Combinatorics,Mathematics

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

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

This page is using the new English version of dCode, *please make comments* !

Sponsored ads

This script has been updated, please report any problems.

Tool to count and generate partial k-permutations. In Mathematics, a partial permutation (or k-permutation) is an ordered list of items. It consists in permutations of each combination.

A partial permutation of k items out of n consist in the list of all possible permutation of each combination of k out of n.

2 items among 3 (A,B,C) can be shuffled in 6 ways: A,B A,C B,A B,C C,A C,B

The counting of the permutations uses combinatorics and factorials

For k items out of n, the number of k-permutations is equal to $$ n!/(n-k)! $$

The list is infinite, here are some examples:

A(2,3) | 6 arranged subsets | (1,2)(2,1)(1,3)(3,1)(2,3)(3,2) |

A(2,4) | 12 arranged subsets | (1,2)(2,1)(1,3)(3,1)(1,4)(4,1)(2,3)(3,2)(2,4)(4,2)(3,4)(4,3) |

A(2,5) | 20 arranged subsets | (1,2)(2,1)(1,3)(3,1)(1,4)(4,1)(1,5)(5,1)(2,3)(3,2)(2,4)(4,2)(2,5)(5,2)(3,4)(4,3)(3,5)(5,3)(4,5)(5,4) |

A(2,6) | 30 arranged subsets | (1,2)(2,1)(1,3)(3,1)(1,4)(4,1)(1,5)(5,1)(1,6)(6,1)(2,3)(3,2)(2,4)(4,2)(2,5)(5,2)(2,6)(6,2)(3,4)(4,3)(3,5)(5,3)(3,6)(6,3)(4,5)(5,4)(4,6)(6,4)(5,6)(6,5) |

A(3,4) | 24 arranged subsets | (1,2,3)(2,1,3)(3,1,2)(1,3,2)(2,3,1)(3,2,1)(1,2,4)(2,1,4)(4,1,2)(1,4,2)(2,4,1)(4,2,1)(1,3,4)(3,1,4)(4,1,3)(1,4,3)(3,4,1)(4,3,1)(2,3,4)(3,2,4)(4,2,3)(2,4,3)(3,4,2)(4,3,2) |

Partial permutations need exponential resources of computer time, so the generation must be paid.

dCode retains ownership of the source code of the script k-Permutations. Except explicit open source licence (free / freeware), any algorithm, applet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any snippet or function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in PHP (or Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the k-Permutations script for offline use, for you, your company or association, see you on contact page !

arrangement,permutation,combination,counting,order,combinatorics

Source : http://www.dcode.fr/partial-k-permutations

© 2016 dCode — The ultimate 'toolkit' website to solve every problem. dCode