Overview

The permutations package provides R-centric functionality for working with permutations of a finite set. It includes group-theoretic composition of permutations and can transform from word form to cycle form and back.

Installation

You can install the released version of permutations from CRAN with:

# install.packages("permutations")  # uncomment this to use the package
library("permutations")
#> 
#> Attaching package: 'permutations'
#> The following object is masked from 'package:stats':
#> 
#>     cycle

The package is maintained on github.

The permutations package in use

Random permutations on a finite set are given by the rperm() command:

rperm(10,9)
#>  [1] (19524)(37)    (1238794)      (1745682)(39)  (15)(3897)(46)
#>  [5] (132654789)    (17263)(59)    (136)(47589)   (162)(4795)   
#>  [9] (14763)(259)   (168347925)

The result is printed in cycle form but we can print in word form if we wish:

options(print_word_as_cycle=FALSE)  # override default
as.word(rperm(10,9,3))
#>      {1} {2} {3} {4} {5} {6} {7} {8} {9}
#> [1]  7   .   .   .   .   .   9   .   1  
#> [2]  .   9   2   .   .   .   .   .   3  
#> [3]  .   .   .   .   .   .   .   .   .  
#> [4]  3   .   1   .   .   .   .   .   .  
#> [5]  .   8   .   .   2   .   .   5   .  
#> [6]  .   .   .   6   .   4   .   .   .  
#> [7]  .   .   .   .   .   .   .   .   .  
#> [8]  .   .   .   8   .   .   .   4   .  
#> [9]  6   .   1   .   .   3   .   .   .  
#> [10] .   .   .   9   .   .   .   .   4
options(print_word_as_cycle=TRUE)  # usually want to print a cycle irregardless

(A dot indicates a fixed point). The package uses arithmetic operations * to combine permutations and ^ for conjugation:

(a <- as.word(c(4,2,3,1,5,7,6)))
#> [1] (14)(67)
(b <- as.cycle(1:4))
#> [1] (1234)
a*b
#> [1] (234)(67)
b*a
#> [1] (123)(67)

The megaminx

The megaminx is a dodecahedral puzzle with similar construction to the Rubik cube puzzle that has 50 movable pieces and 132 coloured stickers (``facets’’). The permutations package includes functionality to simulate the megaminx and exhibits an 82-turn superflip. The vignette gives an extended discussion.