shape | R Documentation |
Returns the shape of a permutation. If given a word, it coerces to cycle form.
shape(x, drop = TRUE,id1 = TRUE,decreasing = FALSE)
shape_cyclist(cyc,id1=TRUE)
padshape(x, drop = TRUE, n=NULL)
shapepart(x)
shapepart_cyclist(cyc,n=NULL)
x |
Object of class |
cyc |
A cyclist |
n |
Integer governing the size of the partition assumed, with
default |
drop |
Boolean, with default |
id1 |
Boolean, with default |
decreasing |
In function |
Function shape()
returns a list with elements representing the
lengths of the component cycles.
Function shapepart()
returns an object of class
partition
showing the permutation as a set partition of
disjoint cycles.
Function padshape()
returns a list of shapes but padded with
ones so the total is the size of the permutation.
shapepart_cyclist()
and shapepart_cyclist()
are low-level
helper functions.
What I call “shape”, others call the “cycle type”, so you will sometimes see “cycle type determines conjugacy class” as a theorem.
Robin K. S. Hankin
size
,conjugate
jj <- as.cycle(c("123","","(12)(34)","12345"))
jj
shape(jj)
shape(rperm(10,9)) # coerced to cycle
a <- rperm()
identical(shape(a,dec=TRUE),shape(a^cyc_len(2),dec=TRUE))
data(megaminx)
shape(megaminx)
jj <- megaminx*megaminx[1]
identical(shape(jj),shape(tidy(jj))) #tidy() does not change shape
allperms(3)
shapepart(allperms(3))
shapepart(rperm(10,5))
shape_cyclist(list(1:4,8:9))
shapepart_cyclist(list(1:4,8:9))
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