permutations (version 1.1-5)

size: Gets or sets the size of a permutation

Description

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

Usage

size(x)
addcols(M,n)
# S3 method for word
size(x)
# S3 method for cycle
size(x)
# S3 method for word
size(x) <- value
# S3 method for 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

Author

Robin K. S. Hankin

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.

Function size<-.word() [as in size(x) <- 9] trims its argument down with trim() and then adds fixed elements if necessary. Compare addcols(), which works only on permutations in word form.

See Also

fixed

Examples

size(as.cycle(c("(17)","(123)(45)")))  # should be 7

x <- as.word(as.cycle("123"))
print_word(x)
size(x) <- 9
print_word(x)


size(as.cycle(1:5) + as.cycle(100:101))

size(id)