conjugate {permutations} | R Documentation |
Are two permutations conjugate?
Description
Returns TRUE
if two permutations are conjugate and FALSE
otherwise.
Usage
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.
The group action of conjugation, that is x^y
or y^-1 x
y
, is documented at conjugation.
are_conjugate(x,conjugate(x^y))
is always TRUE
.
Author(s)
Robin K. S. Hankin
See Also
Examples
as.cycle("(123)(45)") %~% as.cycle("(89)(712)") # same shape
as.cycle("(123)(45)") %~% as.cycle("(89)(7124)") # different shape
are_conjugate(rperm(20,3),rperm(20,3))
rperm(20,3) %~% as.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)))))