size: Gets or sets the size of a permutation

In permutations: The Symmetric Group: Permutations of a Finite Set

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 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.

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.

Author(s)

Robin K. S. Hankin

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)

permutations documentation built on Sept. 11, 2024, 6:10 p.m.