The identity permutation

The identity permutation leaves every element fixed

Usage

is.id(x)
is.id_single_cycle(x)
# S3 method for class 'cycle'
is.id(x)
# S3 method for class 'list'
is.id(x)
# S3 method for class 'word'
is.id(x)

Arguments

x

Object to be tested

Details

The identity permutation is problematic because it potentially has zero size.

Value

The variable id is a cycle as this is more convenient than a zero-by-one matrix.

Function is.id() returns a Boolean with TRUE if the corresponding element is the identity, and FALSE otherwise. It dispatches to either is.id.cycle() or is.id.word() as appropriate.

Function is.id.list() tests a cyclist for identityness.

Author

Robin K. S. Hankin

Note

The identity permutations documented here are distinct from the null permutations documented at nullperm.Rd.

See also

is.derangement,nullperm

Examples

is.id(id)
#> [1] TRUE

as.word(id)  # weird
#> [1] ()
#> [coerced from word form]

x <- rperm(10,4)
x[3] <- id
is.id(x*inverse(x))
#>  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE