# permutations v1.0-9

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## The Symmetric Group: Permutations of a Finite Set

Manipulates invertible functions from a finite set to itself. Can transform from word form to cycle form and back.

## Readme

# 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.

## Functions in permutations

Name | Description | |

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 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 | 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 | |

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## Vignettes of permutations

Name | ||

megaminx_net.pdf | ||

megaminx_net.svg | ||

permutations.Rnw | ||

permutations.bib | ||

start.jpg | ||

superflip.jpg | ||

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## Last month downloads

## Details

Type | Package |

License | GPL-2 |

VignetteBuilder | knitr |

URL | https://github.com/RobinHankin/permutations |

BugReports | https://github.com/RobinHankin/permutations/issues |

NeedsCompilation | no |

Packaged | 2020-11-12 20:08:31 UTC; rhankin |

Repository | CRAN |

Date/Publication | 2020-11-12 21:40:02 UTC |

suggests | knitr |

imports | magic , numbers , partitions (>= 1.9-17) |

Contributors | Paul Egeler |

#### Include our badge in your README

```
[![Rdoc](http://www.rdocumentation.org/badges/version/permutations)](http://www.rdocumentation.org/packages/permutations)
```