# partitionsCount: Number of Partitions/Compositions In RcppAlgos: High Performance Tools for Combinatorics and Computational Mathematics

 partitionsCount R Documentation

## Number of Partitions/Compositions

### Description

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.

### Usage

``````partitionsCount(v, m = NULL, repetition = FALSE,
freqs = NULL, target = NULL)

compositionsCount(v, m = NULL, repetition = FALSE,
freqs = NULL, target = NULL, weak = FALSE)
``````

### Arguments

 `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`). `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.

### Value

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

### Note

When the number of results exceeds `2^{53} - 1`, a number of class `bigz` is returned.

`partitionsGeneral`, `compositionsGeneral`

### Examples

``````## Same interface as partitionsGeneral
partitionsCount(25, 5)
compositionsCount(25, 5, TRUE)
partitionsCount(15, 7, TRUE)
partitionsCount(25, 5, freqs = rep(2, 25))

## Return object of class 'bigz'
partitionsCount(2500, 15, TRUE)
compositionsCount(2500, 15, TRUE)
``````

RcppAlgos documentation built on Oct. 3, 2023, 1:07 a.m.