getpermutationnumber {TUGLab} | R Documentation |
Get permutation number
Description
Given a permutation, this function returns its position in the Lehmer code order.
Usage
getpermutationnumber(permutation)
Arguments
permutation |
A permutation, as a vector. |
Details
The Lehmer code makes use of the fact that there are n!
permutations of a sequence of n
numbers.
If a permutation \sigma
is specified by the sequence (\sigma_{i})_{i=1}^{n}
, its Lehmer code is the
sequence L(\sigma)=(L(\sigma)_{i})_{i=1}^{n}
, where L(\sigma)_i=|\{j>i:\sigma_j<\sigma_i\}|
.
The position of permutation \sigma
according to the Lehmer code order is
L_{\sigma}=1 + \sum_{i=1}^{n} (n-i)! L(\sigma)_i
.
Value
The position of the permutation according to the Lehmer code order, as an integer.
See Also
Examples
getpermutationnumber(c(1, 2, 5, 4, 3))
[Package TUGLab version 0.0.1 Index]