id: The identity permutation

Description Usage Arguments Details Value Note Author(s) See Also Examples

Description

The identity permutation leaves every element fixed

Usage

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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.

Note

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

Author(s)

Robin K. S. Hankin

See Also

is.derangement,nullperm

Examples

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is.id(id)

as.word(id)  # weird

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

Example output

Attaching package: 'permutations'

The following object is masked from 'package:stats':

    cycle

[1] TRUE
[1] ()
 [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE

permutations documentation built on Nov. 13, 2020, 1:14 a.m.