shape: Shape of a permutation

Description

Returns the shape of a permutation. If given a word, it coerces to cycle form.

Usage

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)

Value

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.

Arguments

x: Object of class cycle (if not, coerced)
cyc: A cyclist
n: Integer governing the size of the partition assumed, with default NULL meaning to use the largest element
drop: Boolean, with default TRUE meaning to unlist if possible
id1: Boolean, with default TRUE in function shape_cyclist() meaning that the shape of the identity is “1” and FALSE meaning that the shape is NULL
decreasing: In function shape(), Boolean with default FALSE meaning to return the cycle lengths in the order given by nicify_cyclist() and TRUE meaning to sort in decreasing order

Author

Robin K. S. Hankin

Examples

Run this code


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))