partitions {calculus} R Documentation

## Integer Partitions

### Description

Provides fast algorithms for generating integer partitions.

### Usage

```partitions(n, max = 0, length = 0, perm = FALSE, fill = FALSE, equal = T)
```

### Arguments

 `n` positive integer. `max` maximum integer in the partitions. `length` maximum number of elements in the partitions. `perm` logical. Permute partitions? `fill` logical. Fill partitions with zeros to match `length`? `equal` logical. Return only partition of `n`? If `FALSE`, partitions of all integers less or equal to `n` are returned.

### Value

`list` of partitions, or `matrix` if `length>0` and `fill=TRUE`.

### References

Guidotti, E. (2020). "calculus: High dimensional numerical and symbolic calculus in R". https://arxiv.org/abs/2101.00086

### Examples

```### partitions of 4
partitions(4)

### partitions of 4 and permute
partitions(4, perm = TRUE)

### partitions of 4 with max element equal to 2
partitions(4, max = 2)

### partitions of 4 with 2 elements
partitions(4, length = 2)

### partitions of 4 with 3 elements, fill with zeros
partitions(4, length = 3, fill = TRUE)

### partitions of 4 with 2 elements, fill with zeros and permute
partitions(4, length = 2, fill = TRUE, perm = TRUE)

### partitions of all integers less or equal to 3
partitions(3, equal = FALSE)

### partitions of all integers less or equal to 3, fill to 2 elements and permute
partitions(3, equal = FALSE, length = 2, fill = TRUE, perm = TRUE)

```

[Package calculus version 0.3.1 Index]