permorder: The order of a permutation

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

The order of a permutation

Description

Returns the order of a permutation P: the smallest strictly positive integer n for which P^n is the identity.

Usage

permorder(x, singly = TRUE)

Arguments

x	Permutation, coerced to cycle form
singly	Boolean, with default TRUE meaning to return the order of each element of the vector, and FALSE meaning to return the order of the vector itself (that is, the smallest strictly positive integer for which all(x^n==id)).

Details

Coerces its argument to cycle form.

The order of the identity permutation is 1.

Note

Uses mLCM() from the numbers package.

Author(s)

Robin K. S. Hankin

See Also

sgn

Examples

x <- rperm(5,20)
permorder(x)
permorder(x,FALSE)

stopifnot(all(is.id(x^permorder(x))))
stopifnot(is.id(x^permorder(x,FALSE)))

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