Tool to calculate the rank of a permutation of a set. The permutation's rank is the number associated with it in the order of generation of the permutations.

Rank of a Permutation - dCode

Tag(s) : Mathematics, Combinatorics

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

Tool to calculate the rank of a permutation of a set. The permutation's rank is the number associated with it in the order of generation of the permutations.

To find the row of a permutation, list all possible permutations and sort them in ascending order.

Let the set 'A, B, C', then the permutations are:

0 | ABC |

1 | ACB |

2 | BAC |

3 | BCA |

4 | CAB |

5 | CBA |

The permutation BAC is at number 2 (starting at 0)

Since it seems difficult to list all permutations when there are many items. There is a mathematical method to perform this calculation.

Consider a permutation \( P \) in the set \( E \) of size \( t \).

Consider the permutation B,A,C in the initial set A,B,C of size \( t = 3 \).

For each letter, calculate the position \( p \) in the set \( E \), calculate \( s = p \times (t-1)! \) and remove the letter from the set \( E \) (size \( t \) decreases). The sum of \( s \) is the rank of the permutation.

B is in position \( 1 \) in ABC, \( s_B = 1 \ times 2! = 2 \)

A is in position \( 0 \) in AC, \( s_A = 0 \ times 1! = 0 \)

C is in position \( 0 \) in C, \( s_C = 0 \ times 0! = 0 \)

BAC is at permutation rank \( s_B + s_A + s_C = 2 + 0 + 0 = 2 \)

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

permutation,rank,order,index,number,arrangement

Source : http://www.dcode.fr/permutation-rank

© 2017 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode