`partitionsCount.Rd`

Calculate the number of partitions/compositions of a vector chosen \(m\) at a time with or without replacement. Additionally, these functions can calculate the number of partitions of multisets.

```
partitionsCount(v, m = NULL, ...)
compositionsCount(v, m = NULL, ...)
# S3 method for default
partitionsCount(v, m = NULL, repetition = FALSE,
freqs = NULL, target = NULL, ...)
# S3 method for default
compositionsCount(v, m = NULL, repetition = FALSE,
freqs = NULL, target = NULL, weak = FALSE, ...)
# S3 method for table
partitionsCount(v, m = NULL, target = NULL, ...)
# S3 method for table
compositionsCount(v, m = NULL, target = NULL, weak = FALSE, ...)
```

- v
Source vector. If

`v`

is a positive integer, it will be converted to the sequence`1:v`

. If`v`

is a negative integer, it will be converted to the sequence`v:-1`

. Only integer and numeric vectors are accepted.- m
Width of the partition. If

`m = NULL`

, the length will be determined by the partitioning case (*e.g.*When we are generating distinct partitions of \(n\), the width will be equal to the smallest \(m\) such that`sum(1:m) >= n`

).- ...
Further arguments passed to methods.

- repetition
Logical value indicating whether partitions/compositions should be with or without repetition. The default is

`FALSE`

.- freqs
A vector of frequencies used for producing all partitions of a multiset of

`v`

. Each element of`freqs`

represents how many times each element of the source vector,`v`

, is repeated. It is analogous to the`times`

argument in`rep`

. The default value is`NULL`

.- target
Number to be partitioned. If

`NULL`

,`max(v)`

will be used.- weak
(Compositions only) Logical flag indicating whether to allow terms of the sequence to be zero.

A numerical value representing the total number of partitions/compositions.

When the number of results exceeds \(2^{53} - 1\), a number of class `bigz`

is returned.

```
## Same interface as partitionsGeneral
partitionsCount(25, 5)
#> [1] 30
compositionsCount(25, 5, TRUE)
#> [1] 10626
partitionsCount(15, 7, TRUE)
#> [1] 21
partitionsCount(25, 5, freqs = rep(2, 25))
#> [1] 148
## Return object of class 'bigz'
partitionsCount(2500, 15, TRUE)
#> Big Integer ('bigz') :
#> [1] 4188807783906550542066742
compositionsCount(2500, 15, TRUE)
#> Big Integer ('bigz') :
#> [1] 4097094997743241086270928785678827376
```