# size: Gets or sets the size of a permutation In permutations: The Symmetric Group: Permutations of a Finite Set

## Description

The ‘size’ of a permutation is the cardinality of the set for which it is a bijection.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```size(x) addcols(M,n) ## S3 method for class 'word' size(x) ## S3 method for class 'cycle' size(x) ## S3 replacement method for class 'word' size(x) <- value ## S3 replacement method for class 'cycle' size(x) <- value ```

## Arguments

 `x` A permutation object `M` A matrix that may be coerced to a word `n,value` the size to set to, an integer

## Details

For a `word` object, the size is equal to the number of columns. For a `cycle` object, it is equal to the largest element of any cycle.

Function `addcols()` is a low-level function that operates on, and returns, a matrix. It just adds columns to the right of `M`, with values equal to their column numbers, thus corresponding to fixed elements. The resulting matrix has `n` columns. This function cannot remove columns, so if `n<ncol(M)` an error is returned.

Setting functions cannot decrease the size of a permutation; use `trim()` for this.

It is meaningless to change the size of a `cycle` object. Trying to do so will result in an error. But you can coerce cycle objects to `word` form, and change the size of that.

## Author(s)

Robin K. S. Hankin

`fixed`
 ```1 2 3 4 5 6 7``` ```x <- rperm(10,8) size(x) size(x) <- 15 size(as.cycle(1:5) + as.cycle(100:101)) size(id) ```