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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) (132654789)   
#>  [6] (17263)(59)    (136)(47589)   (162)(4795)    (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.

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Version

Install

install.packages('permutations')

Monthly Downloads

331

Version

1.0-9

License

GPL-2

Issues

Pull Requests

Stars

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Maintainer

Robin K S Hankin

Last Published

November 12th, 2020

Functions in permutations (1.0-9)

orbit

Orbits of integers
permorder

The order of a permutation
Ops.permutation

Arithmetic Ops Group Methods for permutations
allperms

All permutations of a given size
cayley

Cayley tables for permutation groups
conjugate

Are two permutations conjugate?
cyclist

details of cyclists
fixed

Fixed elements
fbin

The fundamental bijection
as.function.permutation

Coerce a permutation to a function
c

Concatenation of permutations
rperm

Random permutations
print

Print methods for permutation objects
commutator

Group-theoretic commutator and group action
megaminx

megaminx
derangement

Tests for a permutation being a derangement
inverse

Inverse of a permutation
length

Various vector-like utilities for permutation objects.
get1

Retrieve particular cycles or components of cycles
id

The identity permutation
dodecahedron

The dodecahedron group
permutation

Functions to create and coerce word objects and cycle objects
shape

Shape of a permutation
sgn

Sign of a permutation
permutations-package

tools:::Rd_package_title("permutations")
megaminx_plotter

Plotting routine for megaminx sequences
tidy

Utilities to neaten permutation objects
size

Gets or sets the size of a permutation
valid

Functions to validate permutations
nullperm

Null permutations
perm_matrix

Permutation matrices