The order of a permutation — permorder • permutations

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.

Author

Robin K. S. Hankin

Note

Uses mLCM() from the numbers package.

See also

Examples

x <- rperm(5,20)
permorder(x)
#> [1] 16 19 12 15 36
permorder(x,FALSE)
#> [1] 13680

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