README.Rmd

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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](https://CRAN.R-project.org) with:

```{r}
# install.packages("permutations")  # uncomment this to use the package
library("permutations")
```

The package is maintained on
[github](https://github.com/RobinHankin/permutations).	

# The ```permutations``` package in use

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

```{r, echo=FALSE}
set.seed(0)
```


```{r rperm}
rperm(10,9)
```

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

```{r wordformprint}
options(print_word_as_cycle=FALSE)  # override default
as.word(rperm(10,9,3))
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:

```{r arith}
(a <- as.word(c(4,2,3,1,5,7,6)))
(b <- as.cycle(1:4))
a*b
b*a
```

# 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.