rperm: Random permutations

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

Random permutations

Description

Function rperm() creates a word object of random permutations. Function rcyc() creates random permutations comprising a single (group-theoretic) cycle of a specified length. Functions r1cyc() and rgs1() are low-level helper functions.

Usage

rperm(n=10, r=7, moved=NA)
rpermm(n=20, r=20, moved=NA)
rcyc(n, len, r=len)
r1cyc(len, vec)
rgs1(s)
rgivenshape(n, s, size=sum(s))

Arguments

n	Number of permutations to create
r	Size of permutations
len	Length of cycles in rcyc() and r1cyc()
moved	In function rperm() and rpermm(), integer specifying how many elements can move (that is, how many elements do not map to themselves), with default NA meaning to choose a permutation at random. This is useful if you want a permutation that has a compact cycle representation
vec	Vector of integers to generate a cycle from
s, size	Shape and size of permutations to create

Details

Function rperm() returns a simple vector of random permutations, and rperm() gives a more complicated object.

Function rgivenshape() returns a random permutation with a given shape. Argument s, specifying the shape, can include 1s (ones). Although length-one cycles are dropped from the resulting permutation, it is sometimes useful to include them to increase the size of the result, see examples. If primary argument n is a vector of length greater than 1, it is interpreted as the shape of the permutation, and a single random permutation is returned. Setting print option print_in_length_order to TRUE emphasises that every element of the output of rgivenshape() has the same shape.

Value

Returns a permutation object of class cycle, or class word (rperm())

Note

In function rperm(), argument moved specifies a maximum number of elements that do not map to themselves; the actual number of non-fixed elements might be lower (as some elements might map to themselves). To control the number of non-fixed elements precisely, use function rcyc() or rgivenshape().

Author(s)

Robin K. S. Hankin

See Also

size, print.permutation

Examples

rperm()
as.cycle(rperm(30, 9))
rperm(10, 9, 2)

rcyc(20, 5)
rcyc(20, 5, 9)

rgivenshape(10, c(2,3))     # shape (3,2), size 5
rgivenshape(10, c(2,3,1,1)) # shape (3,2), but size 7

rgivenshape(1:9)

allpermslike(rgivenshape(c(1, 1, 3, 4)))

permutations documentation built on July 13, 2026, 5:07 p.m.