# shape: Shape of a permutation In permutations: The Symmetric Group: Permutations of a Finite Set

## Description

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

## Usage

 ```1 2 3 4 5``` ```shape(x, drop = TRUE,id1=TRUE) shape_cyclist(cyc,id1=TRUE) padshape(x, drop = TRUE, n=NULL) shapepart(x) shapepart_cyclist(cyc,n=NULL) ```

## 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`

## 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.

## Note

Function `shape()` returns the lengths of the cycles in the order returned by `nicify_cyclist()`, so not necessarily in increasing or decreasing order.

## Author(s)

Robin K. S. Hankin

`size`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```shape(rperm(10,9)) # coerced to cycle data(megaminx) shape(megaminx) jj <- megaminx*megaminx stopifnot(identical(shape(jj),shape(tidy(jj)))) #tidy() does not change shape shapepart(rperm(10,5)) shape_cyclist(list(1:4,8:9)) shapepart_cyclist(list(1:4,8:9)) ```

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