# conjugate: Are two permutations conjugate? In permutations: The Symmetric Group: Permutations of a Finite Set

## Description

Returns `TRUE` if two permutations are conjugate and `FALSE` otherwise.

## Usage

 ```1 2``` ```are_conjugate(x, y) are_conjugate_single(a,b) ```

## Arguments

 `x,y,a,b` Objects of class permutation, coerced to cycle form

## Details

Two permutations are conjugate if and only if they have the same shape. Function `are_conjugate()` is vectorized and user-friendly; function `are_conjugate_single()` is lower-level and operates only on length-one permutations.

The reason that `are_conjugate_single()` is a separate function and not bundled inside `are_conjugate()` is that dealing with the identity permutation is a pain in the arse.

## Value

Returns a vector of Booleans

## Note

The functionality detects conjugateness by comparing the shapes of two permutations; permutations are coerced to cycle form because function `shape()` does.

## Author(s)

Robin K. S. Hankin

## See Also

`group_action`,`shape`

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```are_conjugate(rperm(20,3),rperm(20,3)) rperm(20,3) %~% cycle(1:3) z <- rperm(300,4) stopifnot(all(are_conjugate(z,id)==is.id(z))) data(megaminx) stopifnot(all(are_conjugate(megaminx,megaminx^as.cycle(sample(129))))) ```

permutations documentation built on Nov. 13, 2020, 1:14 a.m.