id

0th

Percentile

The identity permutation

The identity permutation leaves every element fixed

Usage
is.id(x)
is.id_single_cycle(x)
# S3 method for cycle
is.id(x)
# S3 method for list
is.id(x)
# S3 method for 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.

See Also

is.derangement,nullperm

Aliases
  • id
  • is.id
  • is.id.cycle
  • is.id_single_cycle
  • is.id.list
  • is.id.word
Examples
# NOT RUN {
is.id(id)

as.word(id)  # weird

x <- rperm(10,4)
x[3] <- id
is.id(x*inverse(x))
# }
Documentation reproduced from package permutations, version 1.0-5, License: GPL-2

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