# count.perms: Count permutations at a distance In PerMallows: Permutations and Mallows Distributions

## Description

Given a distance (kendall, cayley, hamming or ulam), the number of items in the permutations perm.length and distance value d, how many permutations are there at distance d from any permutation? It can be used to count the number of derangements and the permutations with k cycles (Stirling numbers of the first kind)

## Usage

 `1` ```count.perms(perm.length, dist.value, dist.name = "kendall", disk = FALSE) ```

## Arguments

 `perm.length` number of items in the permutations `dist.value` the distance `dist.name` optional. One of: kendall (default), cayley, hamming, ulam `disk` optional can only be true if counting the permutations at each Ulam distance. Insted of generating the whole set of SYT and count of permutations per distance, it loads the info from a file in the disk

## Value

The number of permutations at the given distance

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```count.perms(4,2,"kendall") count.perms(4,2,"ulam") count.perms(4,2,"hamming") count.perms(4,2,"cayley") # The number of derangements of length 6 is computed as follows len <- 6 count.perms(perm.length = len, dist.value = len, dist.name = "h") # The number of permutations with one cycle is computed as follows num.cycles <- 1 count.perms(perm.length = len, dist.value = len - num.cycles, dist.name = "c") ```

### Example output

```Loading required package: Rcpp
 5
 13
 6
 11
 265
 120
```

PerMallows documentation built on May 2, 2019, 6:14 a.m.