derangement: Tests for a permutation being a derangement

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

Tests for a permutation being a derangement

Description

A derangement is a permutation which leaves no element fixed.

Usage

is.derangement(x)

Arguments

x	Object to be tested

Value

A vector of Booleans corresponding to whether the permutations are derangements or not.

Note

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

The identity element is not a derangement, although the (zero-size) identity cycle and permutation both return TRUE under the natural R idiom all(P != seq_len(size(P))).

Author(s)

Robin K. S. Hankin

See Also

id

Examples

allperms(4)
is.derangement(allperms(4))

M <- matrix(c(1,2,3,4, 2,3,4,1, 3,2,4,1),byrow=TRUE,ncol=4)
M
is.derangement(word(M))

is.derangement(rperm(16,4))

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