| permucycle {Tex4exams} | R Documentation |
Matrix representation of the cycles of a permutation.
Description
permucycle returns a matrix containing information of a permutation. See the Value section for details.
Usage
permucycle(x)
Arguments
x |
a permutation |
Value
Given a permutation x of the numbers 1, 2, ..., n, and i with value from 1 to n. permucycle() returns a (n+1) by (n+1) matrix A with
A[1, 1] |
the total number of cycles |
A[(i+1), 1] |
the length of the i-th cycle |
A[(i+1), 2:(n+1)] |
the members of the i-th cycle |
For example, permucycle(c(3,2,1)) will produce the following matrix:
[,1] [,2] [,3] [,4]
[1,] 2 0 0 0
[2,] 2 1 3 0
[3,] 1 2 0 0
[4,] 0 0 0 0
The 2 in the first row means there are two cycles; The second row means there is a cycle of length 2, with members (1,3); The third row means there is a cycle of length 1, with member (2); The fourth row is redundant for this specific case. One can read from the output of permucycle() to obtain cycle notation (13)(2) of the permutation, and other information.
See Also
Examples
permucycle(c(3,2,1))